Roy Hodgson made one change to the side that drew 0-0 with Fulham on Sunday, with James McCarthy replacing Jairo Riedewald in the midfield duo.
As for Ole Gunnar Solskjær, he made four changes to the side with David De Gea left out of the squad completely, and Dean Henderson handed the opportunity to stake his claim as the United number one.
Following a muscular injury, Edinson Cavani also came back into the starting line-up, alongside Eric Bailly and Nemanja Matic.
The Red Devils, who were unbeaten in their previous 20 away games, started the encounter slowly at Selhurst Park.
Eberechi Eze, the conductor to Palace’s attacking impetus, set the play and linked up well with Christian Benteke and Jordan Ayew.
Benteke, who has looked revitalised following his game winner against Brighton & Hove Albion, bullied Harry Maguire and Eric Bailly, winning every early header that was arrowed his way.
But United started to dictate the tempo of the match, with Mason Greenwood and Marcus Rashford striking fear into Palace’s defence at every attack.
Nemanja Matic, who scored the game winner between these two sides in 2017, struck a sweet strike from the edge of the box, taking a wicked deflection and forcing a breath-taking save from Vicente Guaita.
The United onslaught continued, with Marcus Rashford coming close from an arrowed shot from just outside the penalty area. However, much to the relief of Guaita, the ball whistled past the post.
The pressurised bombardment on the Palace goal continued.
Mason Greenwood received the ball on the edge of the Palace box, and although the Englishman was swarmed instantly by four red and blue shirts when he turned his body into a shooting position, the 19-year-old managed to find a gap, poking a shot inches wide of the post.
After a rather subdued 20 minutes, United came close to opening the scoring before half time - but The Red Devils were denied by a crucial block from Joel Ward - who put his body on the line to thwart the ominous Edinson Cavani who was lurking in the background, waiting to pounce.
As the second half began, and the fog started to sweep across Selhurst Park, Jordan Ayew registered Palace’s first shot on target in over 120 minutes of football, as the Ghanaian tested Dean Henderson from close-range.
However, Ayew failed to get enough power behind his effort to worry the United keeper.
Palace’s bursts of inspiration continued to find a way in-behind the United defence.
Eberechi Eze picked up the ball in the centre of the pitch and immediately looked to pick out Jordan Ayew – who had arrowed past Harry Maguire.
After a slight hesitation due to a suspicion of offside, Ayew drove at the United box, stopped in his tracks and looked to pick out the waiting Benteke.
As Ayew pulled the trigger on his pass, Benteke dropped back into a pocket of space on the edge of the box.
Benteke took one look at the ball, set his body to shoot, and as the ball rolled to his feet, he completely mistimed his shot, sending the ball into the deep crevices of the Holmesdale Road end.
As the United kit began to blend in with the heavy south London night sky, Mason Greenwood decided to take the game to Palace, dancing his way through the Eagles’ backline and setting himself up on the edge of the box.
However, much to the frustration of Greenwood, he could only direct his shot just over Guaita’s goal.
The peppering continued with Luke Shaw, Daniel James and Scott McTominay going close, but no effort really troubled the Palace goalkeeper.
The last chance of the game fell to Patrick van Aanholt.
The left-back found himself of acres of space, gallivanting into the United penalty area. Van Aanholt took one touch to breeze past Aaron Wan-Bissaka and set his sights on goal.
However, the Dutchman hammered his shot straight at Dean Henderson and allowed United to walk away from Selhurst Park with a point.
A toothless United
Ahead of a make-or-break week for Ole Gunnar Solskjær, his tired United side produced a toothless display this evening and failed to ignite a creative spark against a resilient Palace side.
Marcus Rashford was left mute by a rampant Joel Ward – who harried and hustled at any opportunity.
As for Cavani, Greenwood and Bruno Fernandes, the trio were limited to long shots from the edge of the box and were drowned in a deluge of red and blue any time they received the ball.
Although they are 14-points behind Manchester City in the Premier League title chase, the Europa League tie against A.C Milan will be a tough test for the Red Devils.
Palace lacked creativity, but the defensive display pleased Hodgson
A hard fought point pleased Roy Hodgson, who said after the game, "I am not going to sit here and suggest we should have won or done more than we did.
"The 0-0 was a result we fully deserved, but there were some very good signs tonight about us getting back some composure. Nice to see that coming back, playing through the midfield."
Palace face Tottenham Hotspur on Sunday with the 73-year-old manager 'optimistic' that talisman, Wilfried Zaha, will be back for the game.