Juan Mata gave the home side a 47th minute lead but Clint Dempsey levelled for Fulham in the 56th minute and Martin Jol's visitors stood firm to claim a much-needed point.
This was Chelsea's third successive draw, coming on the back of stalemates against Wigan and Tottenham, and denied Andre Villas-Boas's side the chance to force their way back into the title race.
Instead, another disappointment means they sit fourth, two points ahead of fifth-placed Arsenal 24 hours before the Gunners face Wolverhampton Wanderers.
Having moved to within seven points of leaders Manchester City following victory over Roberto Mancini's side earlier in December, Chelsea have fallen well off the pace.
Villas-Boas restored Fernando Torres and Frank Lampard to his starting line-up, giving both the opportunity to restate their claims to a more regular start after being left on the bench for the Blues' more important games recently.
Torres in particular was unlucky not to mark his return with a goal when he carved out his side's best chance of the first half after 15 minutes.
The striker did everything right after being picked out by a floated cross from his fellow Spain international Mata, cushioning the ball on his chest before hooking an acrobatic volley that was superbly saved by Fulham keeper David Stockdale.
Torres's effort came moments after Orlando Sa had spurned a much more clear-cut opportunity to open the scoring for Fulham with the striker heading from just six yards.
Those two chances proved to be the highlights of a disappointing first half that rarely sparked into life and that was played out in a tepid atmosphere that belied the game's status as a derby played out by west London neighbours.
Fulham lost 5-0 to Manchester United in their last match, but if they had been successful in repairing fractured confidence in the opening period, they reverted to type immediately after the restart, allowing Chelsea quickly to take control of the game through Mata.
The 47th minute move began with Ashley Cole on the left before the left back found Torres with his back to goal inside the Fulham area.
Torres rolled the ball back towards Mata and the former Valencia playmaker beat Stockdale with a crisp, left foot shot from the edge of the area.
Chelsea failed to build on Mata's effort, however, and were hauled back when a suspect defence contributed to Dempsey's 56th minute equaliser.
Bryan Ruiz was the creator of the goal, collecting Philippe Senderos's header and wrong-footing Chelsea right-back Jose Bosingwa to reach the byline.
Ruiz then pulled back a low cross that was turned home by Dempsey from close range after the American found space between Terry and Luiz.
Chelsea responded by dominating possession in the final half hour although they were unable to apply enough pressure to conjure a winning goal.
Villas-Boas introduced Didier Drogba at the expense of Daniel Sturridge, Chelsea's in-form goalscorer, and the Ivorian forced a fine late save from Stockdale with a diving header.
Florent Malouda was also brought on and came twice close to scoring, first from a neat backheel and later from a powerful rising shot.
But Villas-Boas's side was unable to find a winning goal and the final whistle brought a smattering of boos from frustrated home fans.
Chelsea frustrated as Fulham make a point
Advertisement