Manchester United were the only winners as below strength Chelsea failed to overcome the handicap of losing key men John Terry, Joe Cole and Arjen Robben.
To rub salt into their wounds, the under-fire defence were breached with Fulham's second attack in the first half, a half totally dominated in possession terms by the Blues.
Fulham can count themselves unlucky that they did not finish off Chelsea in the second half when the league champions looked tired.
Fulham's livewire winger Wayne Routledge could have given the visitors a dream start within two minutes, but the former Crystal Palace star shot wide from just outside the penalty area.
But they did take the lead against the run of play on 17 minutes. Winning a throw on the left, it was quickly taken and the ball fed to Moritz Volz.
The midfielder took one step forward into the Chelsea penalty area before hitting a low, right-footer on target.
Unluckily for Chelsea the ball deflected off the right shin of Ricardo Carvalho and squeezed between the despairing dive of Henrique Hilario and the keeper's right post.
Chelsea, as champions, regained their composure and reacted well to the setback but can count themselves fortunate in the manner of their equaliser.
With 10 minutes remaining of the first half, Claude Makelele sent in a hopeful punt and the ball dropped kindly to Frank Lampard.
The skipper, in the absence of Terry, let fly with a trademark right-footer which took a wicked deflection off the body of Fulham right-back Liam Rosenior. Antti Niemi was helpless as the ball sailed into his goal.
This should have spurred Chelsea into finishing off their rivals, but it was Fulham that could have regained the lead within seconds of the restart only for Hilario to make an excellent save from the header of forward Brian McBride.
Jose Mourinho signalled his intent by bringing on £30million misfit Andriy Shevchenko on 58 minutes, but he might as well have left him on the bench for all the good it did.
But Chelsea have shown in the past that when they are not playing well, they can produce the unexpected and they did this on 62 minutes by taking the lead.
For once Lampard found some freedom in the Fulham penalty area and sent across a deft chipped cross. This was met expertly by Drogba who directed his powerfully struck header from six yards past the hapless Niemi.
Fulham boss Chris Coleman reacted to the goal in a positive manner bringing on striker Luis Boa Morte a couple of minutes later.
And, with 10 minutes remaining, Hilario made a hash of a clearance leaving Routledge with the simple task of tucking the ball home. Unluckily for him the ball inched wide of the Chelsea net.
But Fulham were not to be denied the share of the spoils and with seven minutes left got their reward. Not for the first time, the Chelsea defence was poor as they failed to react to a straightforward cross into their area.
The ball bobbled around before McBride sent in a low drive which Hilario did well to kick clear.
But the ball fell to Carlos Bocanegra who coolly tucked home from four yards to deny Chelsea a three vital points.