Sturridge had not scored against the Cottagers during his time at the club's local rivals Chelsea or while he was at Manchester City, but he took Martin Jol's team apart with three well-taken strikes.
Three minutes after Dimitar Berbatov had nodded Fulham ahead, the England striker turned Aaron Hughes inside-out before smashing the ball into the roof of the net.
The 23-year-old latched on to Philippe Coutinho's deflected pass before beating Fulham goalkeeper Mark Schwarzer to make it 2-1 and he rounded off the win at the death with a clever chip over the Australian stopper, who was playing possibly his last match for the club.
Fulham's final game of the season ended with boos from the Craven Cottage crowd after they saw their team extend their losing streak to five games.
Fulham barely had a touch of the ball in the opening half-hour, but they went ahead after 32 minutes.
Damien Duff tapped the ball to Riether, who appeared to be in an offside position, and he whipped the ball to the back post where Berbatov nodded in after slipping in between Glen Johnson and Jamie Carragher.
The lead lasted just three minutes and 15 seconds. Andre Wisdom punted the ball upfield, Sturridge picked the ball out of the sky with his right boot and lifted it over Hughes before rifling into the roof of Schwarzer's goal.
Two minutes later and Liverpool were ahead for the first time. Coutinho's deflected pass fell into Sturridge's path and he calmly stroked the ball past Schwarzer.
Liverpool substitute Fabio Borini hit a post after giving his marker the slip before Sturridge scored the goal which ensured he took home the match ball, latching on to Coutinho's through-ball and lifted the ball over Schwarzer for what was his sixth goal in his last four matches.