Juan Mata nutmegs Raul Albiol with incredible skill
United fell behind to goals from Andros Townsend and Patrick van Aanholt either side of half-time.
But Jose Mourinho’s side sprung into life with 30 minutes left as Chris Smalling pulled one back before Romelu Lukaku levelled the scores with 15 minutes on the clock.
Christian Benteke had a chance to restore Palace’s lead only for David de Gea to deny him with a spectacular stop.
And it was an unlikely source in United’s team that came up with the late winner.
A loose ball fell to Nemanja Matic on the edge of the box and the Serbia international unleashed a fierce strike into the top corner to send the away supporters crazy.
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Gary Neville was hugely impressed by Juan Mata against Crystal Palace
“I won’t say I’ve always been his biggest fan in terms of… I always thought United’s wide players or the No 10s should be people who can get from box-to-box quite quickly.
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Gary Neville hasn't always been a fan of Juan Mata
“But what United have now with Martial, Rashford, Lukaku, Lingard and Sanchez are players who can get box to box.
"What they have not got necessarily are people who can glue it together. He is the one who can slow it down, who can connect things and can actually link things.
“I thought he made a massive difference in composing United in the final third. He was the one who controlled the ball in the box and made the right decisions."