Didier Drogba was sent off and John Terry suffered a suspected fractured cheekbone as Chelsea made it four games without a Premier League victory.
Drogba was starting to look lively when he was sent off
Drogba, back after a month out with a knee injury, looked lively following a subdued first half from the home side.
But after forcing Kasey Keller into a save he received a second booking when his boot caught Chris Baird's face.
Salomon Kalou and Joe Cole also went close but Paul Konchesky and Diomansy Kamara nearly won it for Fulham.
It was another day of frustration and looking back to happier times for the Blues, whose fans again chanted former manager Jose Mourinho's name during a tepid first half devoid of real entertainment.
Chelsea suffered a blow before the kick-off when midfielder Michael Essien was ruled out with an injury, while boss Avram Grant sprang something of a surprise by leaving out winger Florent Malouda.
His three-man attack of Kalou, Drogba and the woefully ineffectual Andriy Shevchenko looked disjointed and posed few problems for the visiting defence.
If anything, Fulham, who last won at Stamford Bridge in 1979, could have gone to the break a goal ahead.
Clint Dempsey headed just wide of Petr Cech's far post and referee Martin Atkinson turned down a strong claim for a penalty when Tal Ben Haim headed the ball on to his own hand after a long throw-in.
Drogba's main contribution was failing to get on the end of an inviting centre from the impressive Joe Cole and being booked for insisting Baird had impeded him.
It got worse for Chelsea when Terry, who was hurt in an aerial collision with Dempsey in the first period, had to be replaced at the break by Alex.
Abramovich (centre) sat with the fans for the game against Fulham
They could have gone in front right at the start when their best player Joe Cole surged clear down the right and crossed to Kalou who, put off by his marker, could not get clean enough contact but still managed to scuff the ball at Keller, who palmed it on to the post.
Fulham weathered that burst to exert some pressure of their own and it was no surprise when Grant hauled off Shevchenko and brought on Claudio Pizarro.
Drogba was being well marshalled but showed his first real flash of brilliance just after the hour mark when he controlled the ball and unleashed a rasping drive which Keller did well to push away.
Kalou then headed over from Ashley Cole's cross and wide from a free-kick, while Joe Cole slipped the ball just wide of Keller when put through.
Chelsea were finally on top but they were reduced to 10 men when Drogba raised his boot while challenging Baird for a loose ball and caught the defender flush in the face.
Atkinson had no option but to show a second yellow card and Grant replaced Ashley Cole with Malouda in a desperate bid to snatch victory.
It almost backfired when Konchesky broke free on the left and Cech saved with his feet from the left-back.
And there was still time for Kamara to fluff a glorious opportunity after gliding past Claude Makelele, only to hesitate before shooting past the far post.
Chelsea were greeted by a chorus of boos at the end and the sound of their popular former manager's name ringing around the stadium.
They had done nowhere near enough to dispel the memory of the acrimonious end to his reign.
Chelsea boss Avram Grant:
"We needed a win after not getting one in the last three games. We created many chances, enough to win this game, but we didn't score unfortunately.
"The base is okay, but we want to do better. We haven't played well this year and haven't scored goals.
"Against Hull it was good, we scored four goals, and today we created chances.
"We can play better. It's not been good enough for Chelsea, I'm not happy we didn't take the extra two points, but at least we created many chances."
Fulham boss Lawrie Sanchez:
"We kept a clean sheet for the first time in the Premier League and, as always, you sort one end out and the other one stops.
"We had a couple of chances at the end and I'm disappointed we didn't get the three points. We had two one-on-ones with the keeper.
"We are a decent side. We haven't had great fortune with some of the decisions given against us and haven't defended well at times but we have given everyone a game.
"If we play like that for the rest of the season we'll get points all over the place."
Chelsea: Cech, Belletti, Terry (Alex 46), Ben-Haim, Ashley Cole (Malouda 77), Sidwell, Makelele, Joe Cole, Kalou, Drogba, Shevchenko (Pizarro 54).
Subs Not Used: Cudicini, Ferreira.
Sent Off: Drogba (74).
Fulham: Keller, Baird, Hughes, Bocanegra, Konchesky, Ki-Hyeon (Bouazza 73), Smertin (Murphy 82), Davis, Davies, Healy (Kamara 67), Dempsey.
Subs Not Used: Niemi, Kuqi.
Ref: Martin Atkinson (W Yorkshire).