Damien Delaney's fourth-minute own goal gave the hosts the lead and a second-string Palace side feared the worst. However, despite a succession of chances either side of half-time, Louis van Gaal's side finally sealed the victory ten minutes into the second-half thanks to Matteo Darmian's fierce strike from outside the penalty area.
Pardew rings the changes ahead of cup semi-final but Palace find themselves 1-0 down early on
Alan Pardew selected a weaker team for the game with his attention partially focused on Sunday's FA Cup semi-final against Watford at Wembley. Julian Speroni was rewarded with a first start of the season, while Adrian Mariappa and Martin Kelly came into a new-look back four. Emmanuel Adebayor started following his successful cameo appearance against Arsenal and 17-year-old Luke Dreher was named on the first team substitutes bench for the first time.
For all the lack of experience in the Palace team, it was an almost ever-present player who gifted the Red Devils the lead just four minutes in when Delaney deflected Darmian's cross into his own net.
The Eagles responded straight away when Adebayor failed to convert a difficult chance from twelve yards following excellent work from Wilfried Zaha.
Zaha produces good performance against former club but Eagles fail to find a way through United back four
Zaha enjoyed vast success against Darmian on the right and it seemed that getting the former United winger on the ball at every opportunity would be Palace's only route to goal in the first-half. This almost worked once again when Zaha eased past the Italian full-back and crossed, but the Red Devils defence cleared and sped away on the counter-attack - almost doubling their lead had it not been for Speroni denying Wayne Rooney.
The first-half at Old Trafford almost mirrored the opening period from the Arsenal game just three days earlier; United dominated possession and the majority of the chances, but poor finishing meant van Gaal's side missed golden opportunites to extend their lead - particularly from Rooney and Anthony Martial.
Pardew's side were also just as threatening on the counter-attack and had appeals for a penalty waved away when Darmian bundled Zaha to the ground following an exquisite Yohan Cabaye pass. Chung-yong Lee also enjoyed success on the other side of the pitch against Antonio Valencia, but the Eagles failed to break down a resolute back four.
As the first-half came to its climax, Martial came close to doubling the lead when he struck a sensational drive towards goal but Speroni somehow managed to turn it away from goal.
Palace then broke away following Martial's chance but Lee's final pass was delayed when Adebayor would have been through on goal - much to the annoyance of the Togolese forward.
Darmian goal enough to clinch victory
United needed just ten minutes to extend their lead in the second-half when a corner was cleared to Darmian, who took a touch before firing in his first goal for the club via the post.
The lead was well deserved and van Gaal's almost found a quick third following successive chances for Martial and Rooney.
Pardew responded by replacing Lee with Jordon Mutch, but the game was seemingly already out of sight as United searched for a third goal.
One of the few positives for Palace was the return of James McArthur. The midfielder had missed three months with a ligament injury and although having previously feared his season was over, he replaced Cabaye with just over 20 minutes remaining to boost his fitness credentials ahead of Sunday's semi-final.
The result leaves Palace on 39 points with safety almost secure, but attention now turns to Sunday's FA Cup semi-final against Sanchez Quique Flores' Watford, who have suffered a similarly poor start to 2016.