The points were shared but it will be Fulham that will feel hard done by.
The Londoners came the closet yet to beating United since 1965, and it was only a fine penalty save which kept the visitors in it.
A cat and mouse start saw both sides begin warily.
However, it was difficult to tell which side was which as Fulham strung a series of passes together without breaching the United rearguard.
A Steed Malbranque free kick drifted just over the United bar and Fabien Barthez needed to be quick off his line to clear a throughball with Steve Marlet closing down on him.
For all that United could have gone ahead when Abdes Ouaddou missed a right-wing cross and Juan Veron's pass ping-ponged around the box before Rufus Brevett cleared the danger.
Fulham then struck out of the blue when a cross from the left saw the entire United defence miss the ball only for Marlet to pounce at the far post and stab home a point-blank effort.
In the 40th minute David Beckham's cross was headed on by Phil Neville and Paul Scholes' low drive brought a fine save from Edwin Van der Sar.
Facundo Sava then brought the best out of Barthez with a low-foot drive just before half time.
United equalised after one of the few decent throughballs from Beckham.
Alain Goma and Ouaddou collided with each other in the box and Ole Gunnar Solskjaer cleared up the wreckage with a searing drive past Van der Sar.
A three on two attack then saw Marlet sprint past Laurent Blanc only for the Frenchman to barge the Fulham striker.
The spot kick may have seemed harsh but it took another two minutes for it to be taken after first Blanc and then Barthez were booked for time-wasting.
Malbranque's low penalty was heading for the corner until Barthez flung himself to his left to turn the spot-kick away