A Steve Sidwell goal on 19 minutes gave the bottom side the lead.
Fulham held on until twelve minutes from time, when Robin van Persie equalised, before Michael Carrick handed United the lead just two minutes later.
- Advertisement -
But Darren Bent earned Fulham a point with a goal four minutes into injury time, to seriously damage United's Champions League hopes.
Earlier, a goal from Emmanual Adebayor saw Tottenham Hotspur beat Everton 1-0 at White Hart Lane to move above the Toffees and into 5th in the table.
