The England striker showed his technical finesse in the 21st minute after Philippe Coutinho let Jose Enrique's low cross run past him to Sturridge, who skipped round two Villa defenders and goalkeeper Brad Guzan before poking the ball into the roof of the net with the outside of his left foot.
Sturridge's eighth goal in his last seven Premier League appearances gave Brendan Rodgers' men a second consecutive win after they opened their campaign with a 1-0 win over Stoke. Liverpool has yet to concede a goal andl hosts bitter rival and defending champion Manchester United next weekend.
Liverpool weathered the home side's attacks in the second half and goalkeeper Simon Mignolet made sure the team returned to Mersyside with three points by denying Christian Benteke's shot from the right side of the box with a great save in the 86th minute.
"I think we deserved the win, they put us under some pressure in the second half but we deserved it," Sturridge said. "The manager's philosophy is that we play well as a team and that's what we did. It's nice to score, but it's more important we win."
Arsenal eased its angry fans' concerns about their lack of signings by earning its first points in the Premier League this season with their win at a rain-soaked Craven Cottage.
Germany striker Lukas Podolski scored a brace and Olivier Giroud grabbed his third goal in as many games as Arsenal bounced back from a home defeat against Aston Villa in a convincing manner, looking in total control most of the time.
"I am pleased for him because he hasn't started much recently more because of the balance of the team than his performances," Arsenal manager Arsene Wenger said about Podolski, who has been linked with a move away from the club. "I am pleased because he plays with a lot of spirit and he can score goals. Everybody in the squad loves Lukas and I want to keep him."
In Saturday's other matches, Stoke came from behind to beat Crystal Palace 2-1 while newly-promoted Hull claimed its first win of the season with a 1-0 win over Norwich. Everton was held 0-0 by West Bromwich Albion, Newcastle-West Ham also finished scoreless and Southampton drew 1-1 with Sunderland.
Manchester United hosts Chelsea on Monday in a much-anticipated clash between the clubs' new managers David Moyes and Jose Mourinho.
The comfortable win over Fulham is likely to appease Arsenal fans, who voiced their discontent and concerns after the Villa loss, urging their club to bring in new players.
Wenger is still looking to make a marquee signing before the end of the transfer window, and said re-enforcements could come before the Gunners host North London rival Tottenham next weekend.
"It's possible," Wenger said. "Honestly, I'm not the only one that can decide that because the clubs who sell the players (are involved too). We are on the market, you know that. I know we expect news from us."
Giroud scored the opener in the 14th minute with a left-footed shot from close range and Podolski doubled the visitors' lead four minutes before halftime with an excellent finish. Podolski completed the comfortable victory in the 68th after being set up by Santi Cazorla.
England forward Darren Bent pulled one back for Fulham in the 77th.
It was Fulham's first loss this season after it opened the campaign with a win at Sunderland.
Giroud had also scored in Arsenal's opening 3-1 home loss to Villa and during the 3-0 win at Fenerbahce in the first leg of their Champions League playoff.
Everton's new manager Roberto Martinez is still looking for his first victory with the club following the goalless draw with West Brom and will be rueing his team's missed chances after Marouane Fellaini hit the post late and Seamus Coleman also struck the woodwork.
West Brom goalkeeper Ben Foster also made decisive saves to deny Steven Pienaar, Kevin Mirallas, Coleman, Ross Barkley and Fellaini at Goodison Park.
Everton now has two draws from its opening two games, while West Brom earned its first point despite playing without striker Nicolas Anelka, who is on indefinite compassionate leave after the death of one of his representatives.
Stoke scored twice in four second-half minutes to fight back from a goal down against Palace, leaving the promoted visitors without a point after two games back in the Premier League.
Charlie Adam equalized in the 58th minute after former Arsenal striker Marouane Chamakh, who is trying to revive his career at Palace, scored his first league goal since September 2011. Ryan Shawcross grabbed the winner to give manager Mark Hughes his first win since taking charge over the summer.
At St. James' Park, West Ham kept its unbeaten record while Newcastle earned its first point of the season in an uneventful game. Sunderland is still looking for its first win after Jose Fonte's header earned a point for Southampton in the 88th minute. An early goal from Emanuele Giaccherini had put Paolo Di Canio's men ahead.