A hat-trick from the former Chelsea player condemned the hots to their seventh league game without a win as the visitors ran riot at Craven Cottage on Sunday afternoon
After an impressive opening 30 minutes, the hosts took the lead through a Dimitar Berbatov header shortly after the half-hour mark but Liverpool replied instantly through Sturridge just three minutes later.
The former Chelsea player scored again in the second half to double his and Liverpool's tally, before the job was completed with a beautiful flick over Mark Schwarzer.
Brendan Rodgers made three changes to his Liverpool side, bringing in Andre Wisdom, Sebastian Coates and Jonjo Shelvey to replace Daniel Agger, Jose Enrique and club captain Steven Gerrard.
Martin Jol, meanwhile, also made three changes to the Fulham side that lost 4-2 to relegated Reading last weekend, with Phillippe Senderos, John Arne Riise and Urby Emanuelson dropping to the bench to make way for Aaron Hughes, Kieran Richardson and Alexander Kacaniklic.
Sitting just five points clear of the relegation zone with two games left to play and without a win in their last six, Fulham's lacklustre start to their final home game to the season would have done little to fill the confidence of the Craven Cottage faithful.
Richardson's injury woes seem to be never-ending and he had to be replaced by Emanuelson after only 15 minutes, but the Dutchman's introduction led to promising attacking and link-up play between the on-loan left-back and Kacaniklic.
Fulham's determination paid off when Berbatov was able head them into the lead shortly after the half-hour mark thanks to poor marking in the centre of the box from Liverpool.
Sascha Riether was teed up to send a superb cross to the unmarked Bulgarian in front of goal, who put them ahead for the first time in a game since their 3-2 win at home to QPR at the start of April.
Liverpool replied instantly, however, after fantastic play from Sturridge in which he turned one way and then the other to beat Hughes before blasting the ball past Schwarzer to even up the scoreline after a manic three minutes.
Despite conceding so quickly after scoring, Fulham ended the first half on the front foot but Liverpool made sure that the emphasis was with them when the two sides returned onto the pitch after the half time break.
Sturridge started particularly strongly and was handed an early chance to double his tally when Stewart Downing's cross found his head just a minute into the half, but his effort ended up sailing over the bar.
Liverpool set up camp in Fulham's half of the pitch and were determined to stay put, but the hosts fought their way back into the game after early dominance from the visitors and carved out several chances of their own.
Fulham's pressing for an equaliser led to strong shouts for a penalty when Bryan Ruiz's cross struck Lucas' hand on the edge of the six yard box, but referee Mark Halsey waved away the protests.
Liverpool replied immediately to the threat at the other end and, once again, it was Sturridge who finished off an impressive attacking movement when he was picked out in front of goal by a slick pass from Phillippe Coutinho, slotting the ball past Schwarzer to make it 2-1.
The chances continued for the visitors as they picked apart a fragile Fulham defence, but somehow a third goal evaded them, despite their dominance in the final third leading to a host of close chances in which both Downing and substitute Fabio Borini hit the post.
Sturridge was finally rewarded for his, and his team's, efforts when he wrapped up his hat-trick with five minutes left to play, chipping the ball over a fast-approaching Schwarzer after yet another fantastic assist from Countinho.