United got off to a fast start and looked eager to net an early goal, but as it has been so many times this season, a lack of clinical finishing was the problem.
Despite this, Alejandro Garnacho was proving to be the biggest threat for Amorim’s men, as the Argentine cut inside from the left flank but saw his effort was superbly blocked by Chris Richards.
The hosts continued to probe with neat spells of possession, and a swift team move almost brought the opener, but Kobbie Mainoo’s effort cannoned off the left post.
Palace started growing into the contest from here, putting the hosts on the backfoot, and in the first real opening for the Eagles, Tyrick Mitchell’s cross was headed wide by Daniel Munoz, before Maxence Lacroix had a short parried by Andre Onana.
Mitchell himself almost nicked an opening goal as he took advantage of a Lenny Yoro mistake at the back, but the fullback’s shot was deflected wide of the post.
The Londoners were firmly on top going into the break, as Mateta once again powered through the United defence, this time past Harry Maguire, before his chip was tipped wide by Onana.
United initially came out a much better side after the restart, and their gameplan of soaking up pressure and hitting on the counter attacking seemed to be the way that they would cut through Palace.
A swift move upfield saw Amad Diallo break and cut the ball back for Bruno Fernandes, but the United captain’s attempt was well saved by Dean Henderson.
Once again, Palace grew into the contest as the half drew on, with Munoz and Mateta causing all sorts of problems for the hosts’ backline.
The latter has been the talisman for the Eagles since Glasner took over in February 2024, and the Frenchman made it 22 goals in 37 appearances since then when he poked home after Lacroix’s header came off the crossbar.
Amorim threw on both Rasmus Hojlund and Joshua Zirkzee in an attempt to turn the match around, but after Lisandro Martinez had to be stretchered off late on, things went from bad to worse, as Mateta doubled this tally for the afternoon with a simple finish after the ball was laid on a plate by Munoz.
As a result, the Portuguese coach was denied his first set of back-to-back league victories since taking over the troublesome Manchester job.
Victory for Palace lifts them above United in the league table and into 12th place.
Flashscore Man of the Match: Jean-Phillipe Mateta (Crystal Palace)