It could have been even better for the Eagles, had Patrick van Aanholt not spurned the best chance of the game at the end of a Palace counter on 26 minutes.
Both teams saw goals disallowed either side of half time, with Cheikhou Kouyate penalised for offside as Victor Lindelof headed into his own net, and Romelu Lukaku flagged when tapping home the rebound of a Jesse Lingard shot.
Andros Townsend might have won it for Palace had he kept his composure at the end of an adventourous solo run, while Lukaku's header saved by Wayne Hennessey was the closest that United came to pinching all of the points.
Relive how the action unfolded in Manchester with Sports Mole's minute-by-minute updates below.
Subs: Grant, Jones, Valencia, Fellaini, Fred, Sanchez, Rashford
Subs: Guaita, Kelly, Ward, Schlupp, Puncheon, Sorloth, Ayew
Brighton 1-0 Leicester; Everton 0-0 Cardiff; Fulham 2-1 Southampton; Watford 0-0 Liverpool; West Ham 0-3 Man City.