And to make it feel worse for Sir Alex Ferguson's team, Palace were down to ten for the last 30 minutes after Vassilios Lakis collected two yellow cards.
Dropping two points has left Chelsea with a clear lead to land the Premiership title and United must now concentrate on getting a result against AC Milan on Tuesday at the San Siro stadium.
With the Champions League clash in mind, Ferguson started with Wayne Rooney, Cristiano Ronaldo and Paul Scholes on the bench but it was a first start for Ruud van Nistelrooy who had been out for three months with an Achilles injury.
Alan Smith was also back in the starting line-up after an 11-week absence.
A rather untidy first half saw both sides enjoying an equal share of the possession but United had the better of the few chances on offer.
Palace started strongly and earned a couple of early corners, the latter of which caused havoc and it seemed forever before United managed to hack the ball away.
Andy Johnson went down in the box but the referee rightly turned the penalty appeals down, and then Mikele Leigertwood's 20-yard shot forced Tim Howard into making his first save - albeit a routine one.
United were being matched by an energetic Palace performance but they still had a good chance midway through the first half when Ryan Giggs played a short corner to Quinton Fortune.
The South African midfielder crossed perfectly into the goalmouth for van Nistelrooy to connect with a low diving header but Gabor Kiraly changed direction and brilliantly scooped the ball back into the air for Gonzalo Sorondo, fortunately for Palace, to clear.
Palace's livewire Johnson burst through the heart of United's defence only to be hauled down a yard or two outside the area. Michael Hughes then played a short free-kick to Johnson but his shot was blocked and United breathed a sigh of relief.
At the other end, Phil Neville fired a speculative 25-yard shot that Kiraly saved and shortly before the break Sorondo stumbled to give van Nistelrooy space, but he placed his header wide of Kiraly's right post.
After a frustrating time for United, Ferguson decided the time had arrived to bring on Ronaldo and Scholes with the second half just ten minutes old.
Lakis then picked up two yellow cards in quick succession after clumsy tackles – the second on United skipper Roy Keane in the 63rd minute.
Scholes and van Nistelrooy had already forced Kiraly to making flying saves and the crowd could sense ten-man Palace were in for a torrid time.
The last 30 minutes saw United claiming 99 per cent of the play and depleted Palace used Johnson as a lone striker with the rest of the team packed in defence.
United launched attack after attack. Ronaldo volleyed at Kiraly, Giggs curled a free-kick wide of the upright but the chance of the afternoon dropped to van Nistelrooy.
Great play from Scholes, followed by a flick from Rooney, set up the Dutch striker nicely but he made it all too easy for Kiraly in the Palace goal who had to make no more than an ordinary stop to his left. Van Nistelrooy held his head in his hands and quite rightly so.
Palace were hanging on by a whisker as United could do no more than pump balls into the Eagles' goalmouth and send over as many crosses into the goalmouth as they could.
Iain Dowie's men, urged on by the sell-out crowd of over 26,000, played their hearts out. Every clearance upfield was met by approval from the partisan home crowd.
Still Palace's goal was under seige and right at the end, Rooney let fly with a shot from 15 yards, which was half-stopped by Kiraly before falling to Giggs.
The Welsh winger reacted quickly and followed up to reach the ball first, but his rushed attempt looped up in the air and landed on the roof of the net with Kiraly stranded.
It proved to be United's last chance as the title moved nearer to Chelsea's grasp.
MAN OF THE MATCH: Gonzalo Sorondo (Crystal Palace) - A composed and faultless display in the heart of Palace's defence. He made numerous blocks, tackles and clearances to ensure Palace kept a clean sheet against a barrage of United attacks.