Marcus Rashford and Anthony Martial stepped up again to keep United's Champions League ambitions alive with a battling victory at Selhurst Park.
d applied further pressure on Ole Gunnar Solskjaer's Reds with their earlier victory over Sheffield United, but this time United did not blink and responded to remain level on points with the Foxes as a final day showdown looms.
United were made to work hard for the win despite facing a Palace side on a run of five successive defeats. Rashford broke the deadlock after a sluggish start, illuminating an otherwise drab contest for his 22nd of the season. Martial followed suit at the culmination of a glorious team move - inevitably involving Bruno Fernandes - to make the game safe in the 78th minute.
The result extended United's unbeaten run to a nineteenth game, a sequence approaching record territory, but Palace could feel aggrieved after having two decisions marginally go against them.
First, former United man Wilfried Zaha went down under a challenge from Victor Lindelof moments before the Reds took the lead, and Jordan Ayew then thought he had equalised - only for a hare's breadth offside decision to chalk it out.
Palace started the brighter with the enigmatic Zaha at the heart of things. The Palace talisman had the first opening when he turned ex team-mate Aaron Wan - Bissaka and let fly, only for David de Gea to repel the winger's effort. Harry Maguire went close with two headers before de Gea was called into action again, this time to deny Luka Milivojevic from distance at the other end.
Mason Greenwood uncharacteristically miscued but Palace threatened again, this time through leading scorer Ayew, as De Gea sprung to United's rescue again with a smart save with his legs.
Then came the first moment of controversy when Zaha tumbled after a coming together with Lindelof. Replays showed that Lindelof had attempted to play the ball but made contact with the Palace man - whilst it certainly wasn't clear and obvious you have seen them given.
Moments later, United were ahead when Fernandes, who else, picked the key to the lock and opened the door. A perfect pass into Rashford's feet sent the United striker away, shimmying past two defenders before he dummied the advancing Vicente Guaita and rolled the ball in.
Milivojevic went close again with a trademark free-kick, but Ayew looked to have levelled when he turned home at the back post from a Zaha cross.
Subject to the obligatory VAR check, the goal was disallowed with the Eagles feathers ruffled after replays showed Ayew had strayed fractionally offside. A tough call, but a correct decision given the laws of the game.
James McCarthy tried his luck from long range as United's lead increasingly looked a fragile one. Andros Townsend flashed across goal and with memories of United's late draw with Southampton still fresh in the mind, the Reds needed that all important second goal to settle the nerves.
Nemanja Matic had been given a rest but came on to get a hold of midfield, and the Reds immediately looked more assured and cohesive in possession.
Fernandes cracked a scorcher off the post, but the classic clincher duly arrived four minutes later when Rashford burst clear down the left and played a one-two with Fernandes. The Portuguese playmaker swept the ball on to the onrushing Rashford, he touched it back for Martial and the red-hot Frenchman curled home a beauty.
Zaha almost set up another nerve-shredding denouement with a 25-yarder only for De Gea to tip wide, and there were eleven added minutes after a nasty injury to Palace left-back Patrick van Aanholt.
There were no further scares as Untied comfortably saw out a game in which they had started slowly but gradually got better.
Overall team performance: 6/10
United Faithful Man of the Match: Marcus Rashford