A hat trick from the former Chelsea player condemned the Cottagers to their seventh league game without a win as the visitors ran riot in west London
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.
After another strong start from Fulham in the second half, the former Chelsea player then scored again to double his and Liverpool's tally from close range after 63 minutes. The hat trick was completed with a beautiful flick over Fulham goalkeeper Mark Schwarzer with just five minutes left to play.
Sitting just five points clear of the relegation zone with two games to play and without a win in its last six Premier League clashes, Fulham's lackluster start to its final home game of the season would have done little to fill the confidence of the Craven Cottage faithful.
Fulham's determination paid off when Berbatov was able head home after the half-hour mark thanks to poor marking in the center of the box from Liverpool. Sascha Riether, on loan from Cologne, was teed up on the right of the visitor's penalty area by Damien Duff before sending in a superb cross to the unmarked Bulgarian in front of goal.
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 again after a manic three minutes.
Sturridge, seemingly undeterred by the boos from the home fans, started the second half strongly and was handed an early chance to double his tally when Stewart Downing's cross found the England international's head just a minute into the half, but his effort ended up sailing over the bar.
Fulham pressing for an equalizer led to strong shouts for a penalty from the home fans and players alike when Bryan Ruiz's cross struck Lucas' hand on the edge of the six yard box, but referee Mark Halsey waved away the plethora of protests.
In similar fashion to the first half, Liverpool replied immediately to a threat at the other end and, once again, it was Sturridge who finished off an impressive attacking movement. He was picked out in front of goal by a slick pass from Phillippe Coutinho and slotted the ball past Schwarzer from close-range to make it 2-1.
The chances continued for the visitors as they picked apart a fragile Fulham defense, but somehow a third goal evaded them, despite their dominance in the final third.
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.