Substitute Frank Lampard sent Chelsea into the Carling Cup semi-finals with a late winner in a thrilling tie.
Lampard smashed home a vicious low drive that deceived Edwin van der Sar and bounced up off the bar and in.
Damien Duff's deflected shot put Chelsea ahead but Fulham sub Elvis Hammond teed up Brian McBride who turned in the equaliser.
Andy Cole and Pape Bouba Diop hit the woodwork for Fulham but Lampard's late intervention settled it.
Fulham started superbly, eager to show Saturday's lacklustre home reverse against Blackburn was a mere blip and could have been three goals up within five minutes.
Pembridge had a fierce shot blocked by Ricardo Carvalho, McBride was inches away from flicking home Cole's driven cross from the right and Cole then headed just wide with a low glancing header from Pembridge's free-kick.
Sylvain Legwinski also fizzed a shot just wide but, despite Fulham's dominance, they could not find the breakthrough their excellent start merited.
It was not until just after the 15-minute mark that Chelsea, who made six changes from the side that thumped Charlton 4-0 on Saturday, created their first chance.
Duff got free on the right and crossed but Didier Drogba, starting his first match since early October and still looking a little rusty, just failed to connect with the Irishman's teasing cross.
And with Chelsea's flying wingers Duff and Arjen Robben enjoying more and more possession, it was the visitors who looked the more likely as the half wore on.
Robben had the Blues' best opening, but saw his shot beaten away by Edwin van de Sar after jinking past two Fulham defenders.
Duff twice caused mayhem in the home defence but was crowded out before he could pick out a final pass.
Both sides could have snatched a lead seconds before the interval.
First Cole just failed to get on the end of a neat reverse pass from Moritz Volz. And then Drogba was denied by a sensational block challenge from Carlos Bocanegra after Alexei Smertin got free on the left.
The frantic pace continued after the restart and Glen Johnson had a vicious shot beaten away by Van der Sar although the flag was already up as Duff had strayed offside.
Cole then grazed a post with a majestic header following a fine Fulham move, but Chelsea were ahead within seconds of that near miss and it was inevitable both Duff and Robben would be involved.
Robben took the ball deep into Fulham territory and evaded a couple of challenges before finding Duff, whose left-footed 20-yard shot took a wicked deflection off the unfortunate Ian Pearce and bounced down off the turf and over the despairing lunge of Van der Saar.
Chelsea began to stroke the ball about with greater authority but Fulham still threatened and Bouba Diop had a header hit the top of the bar with 23 minutes to go.
Fulham drew level when Malbranque found Hammond, who had only been on the pitch for a matter of seconds, and his low cross was neatly turned in by McBride at the near post.
Smertin wildly blazed over at the other end with the goal gaping, but Chelsea were not to be denied and Lampard won it with a fine low drive that deceived Van der Sar and bounced up and in off the bar.
Fulham: Van der Sar, Volz, Pearce, Rehman, Bocanegra, Diop,
Pembridge, Legwinski, Malbranque, McBride, Cole (Hammond 73).
Subs Not Used: Flitney, Radzinski, Green, Rosenior.
Goals: McBride 74.
Chelsea: Cudicini, Johnson, Ricardo Carvalho, Terry, Bridge,
Smertin, Makelele, Parker, Robben (Cole 62), Duff (Lampard 76),
Drogba (Gudjohnsen 58).
Subs Not Used: Cech, Paulo Ferreira.
Goals: Duff 55, Lampard 88.
Ref: S Dunn (Gloucestershire).