David Stockdale impresses for Martin Jol's side to as Andre Villas-Boas' winless run in London derbies continued after Stamford Bridge's Boxing Day stalemate
Following a tepid first half, Andre Villas-Boas' side took the lead through Juan Mata's curling effort before their visitors struck back in a frustrating afternoon at Stamford Bridge.
The first effort of significance would come from the visitors, as Petr Cech needed to tip Dempsey's dipping effort wide.
Jol's side would then test their hosts again, as Orlando Sa managed to make space for a shot despite being outnumbered by John Terry and David Luiz. The Portuguese striker then spurned a glorious chance to put his side ahead, before some sublime combination play between Chelsea's Spanish contingent.
Juan Mata collected the ball on the right, roughly 30 yards from goal, and cut inside before lifting a weighted pass to Torres. The former Liverpool man took the ball obligingly - controlling it on chest - before volleying at goal only to be denied by Stockdale from close-range.
Despite the tepid nature to the match, neither manager looked to change things during the break, and considering the start his Chelsea made to the second half, Villas-Boas will have been delighted.
Torres tester | Spaniard went close with a well-taken effort on the volley
After making space in the middle of the park, Mata, played to ball to Romeu who then found Ashley Cole on the left. The England left back whipped in a ball which Torres struggled to tame, but the striker pushed the ball on to Mata who curled an effort past Stockdale to put Chelsea ahead.
Fulham's first half display was far from outstanding, although Jol would have been pleased with proceedings. But Mata's strike changed the match, and the visitors looked to hit back quickly.
And that's exactly what they did. Bryan Ruiz sold Cole a dummy on the right side of the box, jinking past the full-back before hitting a low delivery across the face for Dempsey to tap home, as once again Cech looked uncomfortable with players around him.
With 20 minutes left on the clock, Sturridge was replaced by Didier Drogba, who is one short of equalling Chelsea's all-time goals record held by Peter Osgood.
With the game approaching the final 10 minutes, groans of anxiety seemed to echo around Stamford Bridge, as Fulham looked to claim what would have been only their fourth point in this fixture in the Premier League.
As the hosts clocked up their eighth corner of the game, Stockdale continued to stand strong, first denying Meireles before thwarting Drogba.
Chelsea were awarded a free kick in stoppage time, and again Fulham's keeper was on hand to rescue his side. Drogba unleashed a dipping thunderbolt which Stockdale did well to tip over the bar, as Jol's side held on to claim an important point.