The Liverpool striker finished off a flowing first-half move to score his eighth goal in seven league games.
Villa were outplayed early on but improved in the second half, with Liverpool goalkeeper Simon Mignolet twice denying Christian Benteke.
Both sides had late penalty appeals waved away by referee Mark Clattenburg.
Liverpool last won their opening two matches of the season in 2008-9 and this victory means Brendan Rodgers's side extend their unbeaten run to 10 Premier League matches, a streak that began with a win at Villa Park in March.
The platform for victory was set during a first half in which the visitors were utterly dominant. Villa improved markedly after the break but the damage was done.
It has been a brutal start to the season for Paul Lambert's young side. During their magnificent victory at Arsenal and contentious defeat at Chelsea, they displayed tangible signs of progress but against Liverpool they looked flat and, perhaps, fatigued by those two demanding trips to London.
Kolo Toure did well to contain Benteke to just a handful of chances, while Gabriel Agbonlahor only threatened in fits and starts. But Villa's defensive problems remain - this was their 25th successive match without a clean sheet, a record they will look to put right in their next league match against Newcastle in three weeks' time.
Much of the credit must go to Liverpool, though, who once again displayed why there is a growing sense of optimism around Anfield.
The win over Stoke had been Liverpool's first on the opening day since they last mounted a credible title challenge five years ago. It was in that season they last won their opening two matches of a campaign, something they had only done twice in the previous 18 seasons.
There were more signs of encouragement at Villa Park.
Liverpool bossed the opening 45 minutes with a swagger and fluidity that, at times, Villa were unable to contain. Midfielders Steven Gerrard and Lucas Leiva were imperious and Philippe Coutinho was a constant threat as Liverpool's frontline swapped places at will.
His understanding with Sturridge borders on the telepathic. That had been obvious against Stoke and it was that link-up which created Liverpool's opening goal from a move that began with Jose Enrique wide on the left. Coutinho allowed the Spaniard's low cross to run across him and into the path of Sturridge. The former Chelsea striker took the ball around Antonio Luna, beyond the sprawling Brad Guzan and poked it high into the roof of the net with his left foot.
Starved of possession and with the home crowd beginning to grow restless, Villa might have wilted. But as the match wore on, they found a renewed sense of purpose.
Benteke carried their greatest threat and, having escaped the unstinting attentions of Toure, tested Mignolet with a curling shot that his fellow Belgian tipped around the post. Andreas Weimann's effort was then deflected just over the crossbar by Daniel Agger.
Villa began to break free of Liverpool's dominance in midfield and Agbonlahor began to flicker into life. The forward fired narrowly wide, while Benteke was denied a penalty as he collided with Toure following a corner. As with their opening-day win, Liverpool had failed to find a second goal and were now inviting pressure.
Benteke latched onto substitute Nicklas Helenius' header and drew another diving save from the excellent Mignolet. Liverpool might have won a late penalty as Guzan appeared to bring Sturridge down in the area but were happy enough to leave Villa Park with the points.
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Goalkeeper Maarten Stekelenburg injured his shoulder at Sunderland so David Stockdale is set to start.
Arsenal's Laurent Koscielny is banned after his sending off against Aston Villa last weekend.
Nacho Monreal is back in the Gunners' squad, but Alex Oxlade-Chamberlain (knee) has joined a lengthy injury list headed by Thomas Vermaelen (back).
The alarm sirens for Arsene Wenger's reign will be screeching if Arsenal lose back-to-back opening league matches for the first time since the inaugural Premier League season 21 years ago.
If they surrender as meekly as they did against Villa then Fulham can record successive opening Premier League victories for the first time.
But the Gunners reminded everyone that they're not far short of being a really good team when they won handsomely at Fenerbahce in the Champions League on Wednesday.
Arsene Wenger has been overly-cautious in the transfer marker so far, but some of the criticism of him has bordered on the hysterical.
Fans have rightly been frustrated that big-name signings have been mooted yet no deals have been forthcoming. But it's not Wenger's fault that Liverpool wouldn't sell Luis Suarez. The Anfield club told us last week the Uruguayan was never going to move to the Emirates.
Yohan Cabaye's smooth passing and movement would add numbers and quality to midfield, a composed defender like Ashley Williams is a must, while a consistently reliable goalkeeper like Asmir Begovic would be an improvement.
A marquee signing up front would also appease the fans - although actually the side already has plenty of potency with four players reaching double figures last season.
Olivier Giroud will always be unfairly compared to Robin van Persie but his 19 goals from 49 games ratio is a decent return. He scored twice in the home game last season against Fulham, who've never won at Arsenal.
Martin Jol has significantly added bite to his midfield with the signing of Scott Parker. The loaning of Darren Bent is also sharp business.
Fulham certainly have enough quality to stay up, although they will have to end their miserable Spring slump at home where they've lost their last four games.
But Fulham's opening win at Sunderland was flattering. The home side dominated possession and had 14 shots. The Cottagers won it with their only effort.
There is also a lack of pace in key areas of Jol's side. Theo Walcott, supplied by Santi Cazorla, can exploit that. It'll be tight and tense but I can't see Arsenal being beaten again.
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Murray, who is seeded third for the tournament at Flushing Meadows in New York, is in the same half of the draw as world number one Novak Djokovic.
Llodra, 33, is ranked 49th in the world and has been beaten by the 26-year-old Scot in all three previous meetings.
British women's number one Laura Robson, 19, is paired with 32-year-old Lourdes Dominguez Lino of Spain.
Murray last faced left-hander Llodra, a serve-volleyer, at the 2012 Australian Open, when he eased to a straight-sets victory in the last 32.
The Scot, who beat Djokovic in the final of the 2012 US Open and at Wimbledon earlier this summer, would meet the 26-year-old Serb in the semi-finals.
A potential last-eight opponent could be Czech Tomas Berdych, who beat Murray in the quarter-finals of the Cincinnati Open last week.
Argentine Juan Martin Del Potro, winner of the 2009 tournament, is also in Murray's half of the draw and would be a potential quarter-final opponent for Djokovic, who starts against Lithuanian Ricardas Berankis, ranked 126.
Murray, who arrived in New York last Friday, is relishing the prospect of defending a Grand Slam title for the first time.
"It's obviously tough, it's a new experience for me," he said. "This week has been a bit busier than normal, there's been a few more demands on my time.
"I'm looking forward to it. I want the tournament to get started now. I've enjoyed my tennis the last few weeks, but now it's time for business.
"This is a huge tournament for me. I love this tournament and I'll try to have a good run."
The other half of the draw could see a quarter-final between 17-time Grand Slam winner Roger Federer, seeded seventh, and long-time rival Rafael Nadal, the second seed.
Spaniard Nadal opens against American Ryan Harrison, ranked 97, while Swiss Federer faces Slovenian Grega Zemlja, the world number 61.
Likely semi-final opponents for either Nadal or Federer would be Spanish fourth seed David Ferrer or French eighth seed Richard Gasquet.
In the women's draw Robson, ranked 32nd in the world, is seeded 30th for the tournament.
It is the first time Robson has been seeded for a Grand Slam, and she is the first British woman to be a seeded in such an event since Jo Durie at the 1987 Australian Open.
The teenager reached the fourth round in New York last year, a feat she repeated at Wimbledon this summer.
Robson lost in three sets to Lino, currently ranked 53rd in the world, at the US Open in 2010 in their only previous meeting.
British number two Heather Watson will face fellow 21-year-old Simona Halep of Romania, who is seeded 21st.
Watson has seen her ranking slip to 77 after struggling for form following her recovery from glandular fever.
Top seed Serena Williams plays former French Open champion Francesca Schiavone in the first round and has fellow American Sloane Stephens, who beat her at the Australian Open, as a possible fourth-round opponent.
Second seed Victoria Azarenka takes on young German Dinah Pfizenmaier while Maria Sharapova's withdrawal because of shoulder problems means Agnieszka Radwanska is seeded third and Italy's Sara Errani fourth.
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Red Bull's Sebastian Vettel and Ferrari's Fernando Alonso suffered right-rear failures in Friday practice.
The drivers asked race director Charlie Whiting for assurances that Pirelli understands the problem. One senior figure described it as a "big concern".
Pirelli's motorsport director Paul Hembery admitted the tyre failures were "a worry for the sport".
He believes the problems were caused by external damage.
Among the drivers concerned about the issue are three-time world champion Vettel and team-mate Mark Webber plus Alonso, McLaren's Jenson Button and Lewis Hamilton of Mercedes.
Webber said the drivers would not accept Hembery's explanation as a reason for the failures.
"We need answers. And 'debris' is not the answer," the Australian said.
One insider said the drivers were "pretty spiky" about the subject. Webber responded: "We're right to be."
And a team principal, who did not wish to be identified, said: "I'd be amazed if we didn't have to respond to some major issue this weekend."
External damage was Pirelli's explanation after a series of failures at June's British Grand Prix, which led to the company changing the design of its tyres for this race.
Spa is one of the fastest circuits on the calendar, with a series of demanding high-speed corners, and any tyre failure could have serious consequences.
The new tyres are of a more robust construction and were designed with the extreme demands of Belgium's Spa-Francorchamps track in mind.
Over a controversial few days following Silverstone, the Grand Prix Drivers' Association (GPDA) threatened to boycott the subsequent German Grand Prix if there were any further problems.
The failures on Vettel and Alonso's cars on Friday happened in the same area of the Spa track, between Turns 13 and 14 - the Fagnes and Stavelot corners.
These follow shortly after the 150mph Pouhon double left-hander, where the right-rear tyre is put under its highest lateral load for several seconds.
Webber said the concern was not just drivers losing control of their cars in the event of a failure, but being hit by debris if closely following a car when its tyre collapsed.
He made a reference to an incident at Silverstone when Alonso had to take avoiding action at 180mph as a tyre failed on Sergio Perez's McLaren.
"We all know Fernando was very lucky at Silverstone," Webber said. "[Being hit by debris from a tyre at high speed] doesn't bear thinking about."
Webber said the forecasted rain for qualifying and the race on Saturday and Sunday could solve the problem.
Tyres are not under anywhere near as much stress at the slower speeds in the wet.
Hembery showed the media photographs of the damaged tyres.
He said Pirelli had not discovered the cause yet but he believed Alonso's was caused by something on the track and Vettel's by "something caught between the floor and the tyre".
He said: "It's a worry for the sport because we have to go and find out what it is. We will do our best to identify it and what could be causing it."
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The Polish striker tapped home from Marco Reus's cross in the second half.
Dortmund had chances to extend their lead as Nuri Sahin volleyed over before substitute Pierre-Emerick Aubameyang was denied from close range.
Former Wigan striker Franco Di Santo came closest for the visitors, but his powerful drive was kept out late on.
The victory means Dortmund have won their opening three games of the season for the first time since 2001-02, when they went on to win the title.
Bayern Munich were the runaway title winners last season but Dortmund's early season showing suggests the battle for the championship could be a closely-fought affair this season.
They dominated from the beginning of this encounter, but failed to make the most of a host of chances.
Jakub Blaszcyzkowski came closest to breaking the deadlock as he smashed a shot against the crossbar, with Bremen sitting deep inside their own half.
Dortmund found the breakthrough 10 minutes into the second half when Reus's square ball found Lewandowski yards in front of goal and the Poland international was left with a simple finish.
Sahin volleyed over following a scramble in the box and Aubameyang, who scored a hat-trick on his Bundesliga debut earlier this month, saw a low shot denied by Bremen goalkeeper Sebastian Mielitz after racing towards goal.
For all their dominance, Dortmund were almost denied victory late on when Di Santo had sight of goal, but his powerful drive was denied by keeper Roman Weidenfeller.
"In a way it was good that we didn't score earlier, because it would have taken some of the fire out of the players," said Dortmund coach Jurgen Klopp.
"This way, they had their feet on the gas for the whole 90 minutes. Having nine points after only three games and talking about how we can improve is almost a luxury problem.
Klopp added: "I am happy that Lewandowski scored. He was rewarded for having worked as hard as a bull tonight."
Meanwhile, Uefa has launched disciplinary proceedings against Dortmund's Bundesliga rivals Schalke following trouble during Wednesday's Champions League qualifier against Greek side PAOK.
"The allegations against the Royal Blues concern the alleged display of political banners, crowd trouble and late submission of team sheets," Schalke said in a statement on their website. (external)
The club confirmed they are seeking legal advice and will plead not guilty.
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The 25-year-old Brazilian was close to joining Tottenham after having a medical on Wednesday.
But it is understood Chelsea made their move at around 18:00 BST on Thursday, with a fee and personal terms agreed within 24 hours.
Willian will have a medical before his work permit hearing next week.
The transfer was made possible after Chelsea owner Roman Abramovich, whose fellow Russian oligarch Suleyman Kerimov owns Anzhi, intervened.
Willian expected to join Tottenham, but when the Blues stepped in, he felt the chance to play Champions League football was too good to reject.
Sources close to the player said Chelsea have made enquiries or offers for his services in every transfer window since 2011.
Willian will become the Stamford Bridge club's third major summer acquisition following the arrivals of Germany forward Andre Schurrle and Netherlands midfielder Marco van Ginkel.
Earlier on Friday, Blues manager Jose Mourinho indicated that Willian would choose Chelsea over Tottenham.
When asked whether the Brazilian had chosen to join his club, Mourinho nodded.
The Portuguese added: "I know what the player wants, so in this moment we cannot hide."
Willian joined Anzhi in January for a reported £30m after five-and-a-half seasons with Shakhtar Donetsk in Ukraine. But he became available as the Russian club attempt to cut costs after a change in strategy by their owner.
Tottenham had expected to break their transfer record and make Willian their fifth major summer signing.
"I couldn't say much in previous news conferences," Mourinho said.
"I have to answer your questions and try to be honest, but at the same time try to hide a few things.
"I'm happy with my squad, but every one of us managers, we say we are happy, but we are always unhappy.
"We always want something of more quality and we never close the door to the possibility of adding more quality."
Willian's arrival would further strengthen a squad full of attack-minded midfielders, such as Eden Hazard, Oscar, Kevin De Bruyne and Schurrle.
But one playmaker Mourinho insisted would be going nowhere is Juan Mata. Reports in Friday's newspapers said the Spain midfielder, 25, could be offered to Manchester United as part of a bid to sign striker Wayne Rooney.
"No, [it is] speculation. He's a player we all like, he's a player we all want to keep and we want more quality in the team, we don't want less quality," he said.
"We want to add quality. Juan is not a player we want to lose."
Mourinho suggested earlier this week that Chelsea would make a fresh bid for striker Rooney, 27, after their match with Manchester United on Monday.
Asked on Friday how he rated his chances of signing Rooney, Mourinho said: "I don't care. In this moment I don't care. I have a big match to play on Monday."
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Andros Townsend was very impressive that Gareth Bale would have been proud of him.
The 22-year-old scored a superb solo goal to start the rout and he outpaced his marker to supply the assists for Roberto Soldado's first goal of the night and Paulinho's maiden strike for the club.
Danny Rose scored his first goal for Tottenham since his wonder strike against Arsenal in 2010 and Soldado added a second to round off the victory
which almost certainly guarantee's Spurs' progression to the group stages of the competition.
Even though he was some 2,200 miles away from London, Andre Villas-Boas could not escape questions about Bale in the run up to the game, and having seen technical director Franco Baldini despatched to Madrid last night, it appears Spurs are resigned to losing their star man.
Yet there was plenty of reason for the Tottenham manager to be optimistic after this performance in the Georgian capital.
Yes, Dinamo are hardly Champions League quality, but this was a potential banana skin that Tottenham avoided with ease, and there were some impressive displays all over the pitch.
Townsend showed how much his confidence has grown during his year at QPR while new signings Nacer Chadli, Soldado and Paulinho stood out again as they did at Crystal Palace last Sunday.
Even though the 55,000 capacity Dinamo Arena was half-full by kick-off, the noisy home fans gave Spurs players an acrimonious welcome.
The visitors responded well, but neither Soldado nor Gylfi Sigurdsson could take advantage of a moment of nervousness from Dinamo stopper Giorhi Loria.
Sigurdsson then dallied on the ball, allowing the impressive Elguja Grigalashvili to race into the Spurs box, but his shot was deflected over.
Dinamo left themselves exposed at the back from the resulting corner and Townsend took full advantage.
Paulinho's challenge released the England Under-21 international and he sprinted from inside his half before unleashing a low drive past Loria.
The hostile atmosphere subsided and the only audible sound inside the stadium came from the jubilant 100 fans in the away end.
Dinamo went on the attack, Lloris pulled off a superb save to deny Jaba Dvali from eight yards.
The crowd sensed an equaliser, but Dinamo's defensive frailties left them open at the back.
A mix-up between Giorgi Gvelesiani and Davit Kvirkvelia gave Soldado some room in the box, but Loria denied the Spaniard at his near post.
Sigurdsson curled a free-kick in to the side-netting and Loria almost fumbled a Rose cross in to his own
net.
Then, just before the break, Spurs scored another superb goal. Townsend was the inspiration once again, embarrassing Darko Glishich with a sharp turn before chipping the ball to the unmarked Paulinho, who nodded in from eight yards.
The third goal came in the 56th minute and Townsend, inevitably, was the architect.
The winger raced down the right flank, gained a yard on his marker and pulled the ball back for Soldado, who slotted the ball past Loria.
Tottenham's fourth goal was just as pleasing on the eye. Chadli found Rose after cutting in from the left flank and he curled a beautiful shot over Loria from 25 yards.
Dinamo fans started leaving their seats three minutes later after Chadli sent a low cross to the back post and Soldado tapped home from close range.
Giorgi Merebashvili sprinted past three players to find Dvali, but Lloris saved with his legs.
Grigalashvili tested Lloris again with eight minutes left, but he saved well.
Spurs raced up the other end and they almost made it six, but substitute Harry Kane's header hit the woodwork and they had to settle for 5-0 scoreline.
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Wales international Bale, 24, is determined to join the Spanish club.
He has not travelled for Thursday's Europa League tie with Dinamo Tbilisi in Georgia because of a foot problem.
It is an injury that kept Bale out of most of Tottenham's pre-season programme and their Premier League opener at Crystal Palace.
Any deal will not be announced before Real's friendly with Qatar side Al Sadd on Thursday. The match will mark the return of Real legend and leading scorer Raul, who now plays for Al Sadd.
The number 11 shirt, which Bale wears at White Hart Lane, has been left vacant at Real Madrid in the expectation their new record signing will take it on his arrival.
To help compensate for his possible departure, Spurs have twice broken their previous transfer record this summer, recruiting Paulinho from Corinthians for about £17m and Roberto Soldado from Valencia for £26m.
The additional purchases of Nacer Chadli and Etienne Capoue have taken their total outlay to about £60m, while Anzhi Makhachkala attacker Willian is in talks over a £30m move and Roma playmaker Erik Lamela is also rumoured to be part of Spurs' plans.
Bale joined Tottenham for £10m from Southampton in 2007 and scored 26 goals for the north London side last season.
His impressive displays led to him being named player of the year by both the Professional Footballers' Association and Football Writers.
Bale's camp told Spurs at the end of July that he wanted to speak to Real.
Real coach Carlo Ancelotti's subsequent claim that they were "in talks to find a solution" to the transfer angered his Tottenham counterpart Andre Villas-Boas.
But it looks increasingly likely that Bale will become Real's fifth summer signing.
Real Sociedad midfielder Asier Illarramendi and Malaga playmaker Isco have arrived for reported fees of £34m and £23m respectively while Dani Carvajal has signed from Bayer Leverkusen and Casemiro has been given a permanent deal after a loan spell from Sao Paulo.
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The Brazilian's 66th-minute header, his first goal since moving to the La Liga champions from Santos, cancelled out David Villa's opener at the Estadio Vicente Calderon.
Villa's goal was also his first for his new club and came against his former side but Barcelona will go into the second leg on August 28 with the upper hand.
Whether Barcelona superstar Lionel Messi is available for that clash remains to be seen after he came off at half-time with a suspected hamstring injury.
It was Villa who struck with the first real chance of the game as his brilliant finish put Atletico ahead on 12 minutes.
A sweeping counter-attack led to Villa playing a clever pass out wide to Arda Turan and the Turkey international returned the ball to his 31-year-old teammate.
Just inside the area, Villa's volley was exquisitely controlled and found the bottom corner for his first goal in Atletico colours.
Barcelona characteristically controlled possession but struggled to create much against a well-drilled Atletico defence.
Making matters worse for Barca, Messi made way at half-time and was replaced by Cesc Fabregas.
The former Arsenal captain went close to an equaliser four minutes into the second half, moments after Alexis Sanchez was denied by Thibaut Courtois in a one-on-one.
After the Chilean's effort was kept out, he set up Fabregas, who was unable to get a shot away under a last-ditch tackle from Turan.
Clear-cut chances were few and far between for Barca and Andres Iniesta tried his luck from range but his effort was comfortably saved by Courtois.
Diego Costa forced Victor Valdes into a save on the hour-mark before Barcelona equalised through Neymar six minutes later.
The Brazil star had been introduced just seven minutes before he headed in a Dani Alves cross at the back post, after the right-back exchanged passes with Xavi.
Alves' cross was perfectly weighted and Courtois was unable to get across quick enough to keep the header out at his near post.
Barcelona looked the more likely to find a winner and had Xavi curl a free-kick just over on 72 minutes.
Courtois came out quickly to block a Sanchez shot at the back post minutes later as the visitors took control of the contest.
A tired-looking Atletico side were pinned back into their defensive half but they remained compact enough to keep Barcelona at bay.
SIGN
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Sources from both clubs have moved to quash reports that a €109 million fee had been accepted by Spurs chairman Daniel Levy, who is holding out for €117m from the Santiago Bernabeu outfit.
Tottenham are closing in on a €70m double swoop for Roma star Erik Lamela and Anzhi attacker Willian as they anticipate Bale's departure for a world-record fee.
Yet Spurs sources insist that the Welshman will stay at White Hart Lane if the Spanish giants refuse to increase the value and structure of their existing offer, believed to be worth around €100m.
Bale has privately told senior Spurs officials of his desire to move to Madrid, where, he believes, he can fulfill his potential and pursue silverware after having spent six years in north London.
The PFA and FWA player of the year feels that the time is right to move on this summer after Tottenham failed to qualify for the Champions League last season and Levy accepts that a bid approaching the nine-figure mark would be too good to turn down.
Real Madrid president Florentino Perez is set to step up his efforts to sign Bale in the coming days, with the 24-year-old forward not expected to play in August, having missed much of pre-season with minor injury complaints.
Tottenham are trying to sign unsettled Madrid left-back Fabio Coentrao for around €17.5m but claim that negotiations over the Portugal international are independent to any discussions over Bale.
Real and Bale's camp are both confident that a move will go through before the transfer window closes but know that the final decision rests with Levy, who is set to break the £100m barrier for the club's summer spending.
The Spurs chairman, a notoriously fierce negotiator, is determined to build a squad capable of qualifying for the Champions League and even competing for the Premier League title - regardless of Bale's future.
The Londoners have already spent heavily this summer to sign Roberto Soldado, Paulinho, Etienne Capoue and Nacer Chadli, with Willian's arrival from Anzhi Makhachkala for around €35m expected to be confirmed in the next 24 hours.
Spurs are also confident of agreeing a deal for Lamela following a meeting in London on Tuesday between their technical director, Franco Baldini, and Roma chief Walter Sabatini, who values the Argentine at £29.9m.
Baldini knows Lamela well from his time at Roma and the 21-year-old was a major point of discussion when the Italian met his former colleague Sabatini, the sporting director of Roma, in London earlier in August.
Spurs are also thought to have registered an interest in Roma's Miralem Pjanic but the Italian outfit are only willing to offload one of the pair after selling Pablo Osvaldo to Southampton in a deal worth up to €17.2m £15m.
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