Juan Mata's goal midway through the second half was enough for Palace to suffer defeat at Manchester United, but only after a dogged defensive display kept the hosts at bay for the majority of the game.
Mata struck four minutes after being brought on as a substitute to score the game's opening goal, but it could easily have been Palace who took the advantage into half-time when Fraizer Campbell lofted the ball over David de Gea but it went over.
United also saw shots cleared off the line and hit the woodwork during the encounter but ultimately the one goal would prove to be Palace's undoing.
Two minutes into the game Adnan Januzaj ghosted in from the right and thumped a shot towards the top corner but it whistled fractions over, and soon after Angel Di Maria had his first sighter but shot straight at Julian Speroni.
But despite United dominating the possession stats they struggled to carve out opportunities during the opening 20 minutes, although two did come along in the space of a minute midway through the first period.
After Wayne Rooney took aim from distance and ballooned a shot over, Luke Shaw picked the ball up in his own half and marauded forward from the left-back position. He advanced fully 60 yards to get inside the area and get away a shot, and Speroni produced some great reactions to swat his low attempt away.
Palace were holding their own, awaiting an opportunity to pounce and on 39 minutes it came. A long ball by Damien Delaney caused hesitation in the hosts' defence and allowed Campbell the opportunity to go one-on-one with de Gea, and the striker lifted the ball over the goalkeeper but it landed the wrong side of the bar.
Playing at his former club, Campbell then saw a close-range bicycle kick also clear the crossbar as Neil Warnock's side finished the half strongly.
After the break Rooney went close when Paddy McNair brought the ball forward and set-up the England captain but his placed effort drifted just wide of the far post, and then his corner was met by Marouane Fellaini who beat Speroni but not James McArthur who cleared off the line.
The towering Belgian once again got on the end of a Rooney delivery five minutes later but put it well over the top, but 23 minutes from time the pressure finally told as United broke the deadlock.
Having been brought on as a substitute minutes earlier, Mata received the ball just outside the area and after getting it onto his left foot he drilled the ball towards goal, and after taking the slightest of deflections off Delaney it beat Speroni to end the Eagles' resistance.
The Spaniard nearly had a second when van Persie saw a shot blocked by Delaney and it rebounded into his path, but after Scott Dann had thrown himself in front of that the ball cannoned off the post before van Persie shanked another shot wide.
Rooney also put the ball past the post late on but it was Mata's strike that ultimately clinched the points for the Red Devils.
Manchester United: De Gea, Valencia, Blind, McNair (Fletcher 90), Shaw, Carrick, Fellaini, Januzaj (Mata 63), Di Maria (Wilson 71), Rooney, van Persie. Subs not used: Lindegaard, Vermijl, Blackett, Herrera.
Palace: Speroni, Mariappa, Delaney, Dann, Ward, Puncheon, Ledley, McArthur, Bolasie (Gayle 80), Chamakh (Bannan 80), Campbell (Doyle 90). Subs not used: Hennessey, Kelly, Fryers, McCarthy.