The visitors found themselves behind early when a VAR check showed Will Hughes had handled a ball from Rashford in the box, and Bruno Fernandes sent Vincent Guaita the wrong way from the spot in the seventh minute.
As it happened: Man United vs Palace
Palace had their best chance just before the break when Jeffrey Schlupp struck a dipping, swerving shot from distance that David de Gea had to get down smartly to save, but other than that Palace struggled to threaten the United goal.
Rashford cut inside a curled a shot just over the bar 11 minutes into the second half, and shortly afterwards winger Antony sped into the box with the ball at his feet but he couldn’t find a team mate and Palace were able to clear.
The in-form Rashford was not to be denied and he made it 2-0 in the 62nd minute with a simple finish after a move that featured some superb short passing as United looked set to cruise to victory.
FULL-TIME Man Utd 2-1 Crystal Palace10-man Man Utd secure their sixth straight home win in the #PL#MUNCRY https://t.co/nx1a3OOQum
— Premier League (@premierleague) 1675529923000
However, Palace were thrown a lifeline when Casemiro was shown a straight red card for grabbing Hughes by the throat as both sides clashed following a tackle on Antony, and Schlupp pulled a goal back in the 76th minute to give them hope.
The visitors poured forward looking for an equaliser but United coach Erik ten Hag sent on Harry Maguire and Victor Lindelof, who replaced fellow substitute Alejandro Garnacho to help stem the onslaught as they hung on for the win.
Manchester United climbed to third in the standings on 42 points, eight behind leaders Arsenal and three behind second-placed Manchester City, while Palace are 12th on 24 points.