Manchester United failed to capitalise on Chelsea's draw at Arsenal as Papa Bouba Diop's superb 25-yard strike cancelled out Alan Smith's opener.
United started strongly and almost took the lead when first Roy Keane and then Wayne Rooney each smashed long-range shots against the woodwork.
Smith finally made the breakthrough when he robbed Sylvain Legwinski and poked the ball past Edwin van der Sar.
But United were made to pay for wasted chances when Diop equalised late on.
From they way United started, it seemed not if they would win but a question of by how many goals.
Rooney, Gary Neville and Paul Scholes all fired warning shots as United poured forward and easily bypassed Fulham's midfield.
For all his bulk and physical presence, Diop was proving ineffective at repelling wave after wave of attacks.
But the Senegal international did almost haul Fulham back into the game when he forced Roy Carroll into tipping his header over just after the re-start.
But by then, United should have made any Fulham strike a mere consolation, such was their dominance in the first half.
The woodwork twice prevented United before Smith's opener.
Keane thundered a long-range shot against the post and then Rooney cracked an effort that cannoned off the other upright.
A bewildered Fulham seemed helpless and Cristiano Ronaldo fizzed a shot narrowly wide as United fired at will.
The inevitable happened just after the half-hour, when Smith demonstrated his tenacity and eye for goal.
His initial shot was blocked but he retrieved the rebound with a sliding tackle on Legwinski, then beat Liam Rosenior before poking the ball home with his right foot.
After the interval, Fulham moved their defensive line further up the pitch and benefited as United's time on the ball was greatly reduced.
And the visitors' almost lost their lead, too, when former United striker Andy Cole jinked past Rio Ferdinand to crash a sweet strike against the post.
A galvanised Fulham were through again shortly after but Legwinski chose to play the ball across the box rather than shoot and the chance was gone.
Despite retaining less possession than in the first 45 minutes, United still looked menacing when moving forward.
Scholes and Smith were keen to shoot on sight, and Gabriel Heinze went close with a free-kick as Sir Alex Ferguson's men attempted to improve their advantage.
When Diop muscled his way into a position to get a dangerous cross in, only for Brian McBride to misdirect his header, you could see why United may have felt vulnerable.
And the increasingly influential Diop, much-improved after a below-par first half, was destined to have a dramatic late input.
As he picked up the ball on 87 minutes there appeared little danger but he arrowed a long-range strike into the top corner.
It proved enough to earn Fulham a point and frustrate a United side who will rue missed opportunities to wrap the game up in the first half.
Fulham: Van der Sar, Rosenior, Pearce, Rehman, Bocanegra,
Malbranque (John 83), Legwinski (Radzinski 74), Pembridge,
Diop, Cole, McBride.
Subs Not Used: Flitney, Knight, Hammond.
Booked: Diop, Radzinski.
Goals: Diop 87.
Man Utd: Carroll, Gary Neville, Ferdinand, Silvestre, Heinze,
Ronaldo, Keane, Scholes, Giggs, Smith, Rooney.
Subs Not Used: Howard, Bellion, O'Shea, Fletcher, Fortune.
Goals: Smith 33.
Ref: P Dowd (Staffordshire).