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.
follow us on twitter www.twitter.com/sportscyber
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.
follow us on twitter www.twitter.com/sportscyber
