Despite Joel Ward earning them a chance to gain a point when he netted after a Romelu Lukaku brace, Palace were to be defeated when Ashley Young sealed the win for the visitors late in the match.
Early on, the hosts had to suffer a tame, opening scare to spark the clash into life as a bouncing ball fell deep into their half. With Vicente Guaita racing out to claim it, Lukaku was able to head towards an unguarded goal, however Martin Kelly calmly mopped up to cleared the threat.
For the second time, Lukaku came within inches of opening the scoring when, from Luke Shaw's outswinging corner, he appeared unmarked in the centre of Palace's box only to blast narrowly wide from less than 10 yards.
At the other end of the pitch, it was the Eagles who caught their opposition unaware as James McArthur jinked down the left-wing before cutting inside to David de Gea's box where he rolled the ball to Andros Townsend. Frustratingly, the 27-year-old could only blaze wide in a fashion similar to Lukaku.
Inches of the warm evening's air was all that separated the ball and the inside of the net again as Townsend picked up possession on the edge of United's area before launching an effort at goal which went agonisingly close.
But it was United who would find themselves celebrating first after Lukaku, at the third time of asking, found the net with a smart finish from 18 yards which nestled into the unmoved Guaita's net.
Immediately responding following the game's re-start, Townsend whipped in a sublime cross which Jeffrey Schlupp met just a little too softly as he glanced the ball over the bar having launched his head up from very close-range.
Opening the second half, Paul Pogba prodded a header over following Alexis Sanchez's chipped ball and perhaps should have done better with the opportunity.
The Red Devils' dominance yielded a second as Lukaku doubled his tally for the night following a defensive scramble. Guaita flung himself at his feet but the Belgian hooked the ball home even under pressure. Looking to respond, Wilfried Zaha raced to strike home from McArthur's ball, however he was just unable to meet the cross in time.
Zaha came close again for the Eagles when he fancifully stepped his way past Young before unleashing a shot from a tight angle at the near post. De Gea, however, was equal to the effort. For his third chance in as many minutes, Palace's Ivorian midfielder then headed over from the same near post as Selhurst Park inhaled sharply in unison.
Another chance then passed the Eagles by when James Tomkins managed to force a looping header in the direction of goal, though it was slightly too high to open his side's account.
The opener came, however, moments later via an unlikely source. With Palace retaining possession on the edge of United's box under relentless defensive questioning, Schlupp broke free to crack a cross high to his right which Ward hurled himself at with an emphatic outcome.
Palace's resurgence seemed to have been catalysed by a smart substitution that saw Max Meyer take to the turf. Minutes after Ward's flying goal, the German midfielder looked to pull Palace level, but his means of doing so - a fine long-distance shot - were denied comfortably by De Gea.
Seeking to build on his team's momentum, Luka Milivojevic struck a goalbound free-kick just wide before, at the other end of the pitch, Guaita flew to his left where he thumped away a probing effort.
Well on-top by this point, the Eagles were to have their hopes of a comeback shattered when United's captain Young struck home with venom into their net from a shallow angle in the box.
With the game seemingly won, Ole Gunnar Solskjær handed a first-team debut to 17-year-old James Garner who saw out the match with the rest of the United team despite the best efforts of Christian Benteke, who headed low into De Gea's hands with the last chance of the night.
Palace: Guaita, Van Aanholt (Kouyate 83), Tomkins, Kelly, Ward, Schlupp, Milivojevic, McArthur (Meyer 61), Zaha, Batshuayi (Benteke 78), Townsend.
Subs not used: Hennessey, Dann, Riedewald, Ayew.
United: De Gea, Shaw, Lindelof, Smalling, Young, Dalot (Bailly 77), Pogba, McTominay, Fred (Garner 89), Sanchez (Rashford 77), Lukaku.
Subs not used: Romero, Pereira, Rojo, Chong.
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