Lee Clark gave Fulham a third minute lead, Diego Forlan levelled for United just before the break but second-half goals from Steed Malbranque and substitute Junichi Inamoto gave the west Londoners their first win over United since 1964.
Jimmy Floyd Hasselbaink scored Chelsea's first-half winner to put them top on goals scored but level on 23 points with Arsenal, who play at Charlton Athletic on Sunday. United stay third on 22 points.
Elsewhere, Wolverhampton Wanderers produced an astonishing comeback to beat Leicester City 4-3 after trailing 3-0 at the break, Liverpool ended a three-match losing streak by beating Leeds United 3-1 and Newcastle United's revival continued with a 3-0 win over Portsmouth.
But aside from Wolverhampton, the place to be for drama was clearly Manchester.
United, who had not conceded a goal at Old Trafford all season and had not lost at home in the league since September 2002, went into the game as runaway favourites.
But they were rocked by Clark's early goal after a slip by Mikael Silvestre and were saved by the crossbar before Uruguayan Forlan levelled with his first goal since January.
Forlan squandered further chances in the second half and United paid the price when Malbranque, who signed a contract extension on Friday, scored in the 66th minute.
Inamoto made sure of the win in the 79th, when the Japan midfielder pounced on some slack defending to steer the ball past keeper Tim Howard.
Ferguson, who said skipper Roy Keane and fellow midfielder Paul Scholes did not play because they were not fit, told Sky Sports: "We looked lethargic, to be honest --
"We got off to a bad start, it spread right through and the amazing thing was that we went in 1-1 at halftime.
"We controlled the 20-odd minutes until they scored a second goal and after that there was no chance...they deserved their win, there's no question about that."
Fulham's delighted boss Chris Coleman said: "To put that sort of performance in against the champions is brilliant. I think they're the best team in the league and I still think they'll win the championship again.
"But you've got to give credit to our lads, they were top drawer...we showed a lot of heart and a lot of bottle as well to come here and get that result."
Chelsea had Dutch striker Hasselbaink to thank for their win at Stamford Bridge as they bounced back from last weekend's derby defeat by Arsenal.
"It was important to come back and win after getting only one point from two matches in the league," said Chelsea boss Claudio Ranieri. "And we played good football.
"At the end, we suffered. But we suffered as a team."
Michael Owen and substitutes Danny Murphy and Florent Sinama-Pongolle scored the goals that gave Liverpool their first league win since September 20 and eased the pressure on manager Gerard Houllier.
"I think they knew it was an important game for everyone who loves the club and I'm pleased because in terms of effort and football they delivered something special," Houllier told Sky Sports.
As for fielding Owen, who played the first half on his comeback from injury before being replaced by French teenager Sinama-Pongolle, Houllier said: "There was no risk, otherwise I would not have played him.
"Michael is a vital player for us, we know that, he gave a boost probably to the whole team and also maybe to himself."