The injury-ravaged Eagles started well and were rewarded when Andros Townsend swept home an early opener with the aid of a heavy deflection from Victor Lindelöf.
Early in the second half Roy Hodgson's men doubled their lead. Quick thinking from Jeffrey Schlupp at a free-kick just inside the United half released Patrick van Aanholt and the Dutchman strode on before arrowing a rasping effort beyond David de Gea at the near post.
That looked to have set Palace on their way to a first league victory against the Red Devils in 27 years. But United had other ideas.
Chris Smalling kickstarted the comeback with a routine header at the back post after Palace had switched off. Romelu Lukaku then levelled, scoring in consecutive Premier League fixtures for the first time since December.
A remarkable turnaround was completed in stoppage time. The ball fell to Matić 25 yards out and the powerful Serbian crashed a dipping half-volley beyond Wayne Hennessey to snatch victory for Manchester United.
But what did we learn from a dramatic encounter at Selhurst Park?
Mou got it
After a listless first half Manchester United boss José Mourinho was out several minutes before his players at the start of the second period. Whatever wisdom the Portuguese had imparted on his side, the final few seconds spent discussing it in the tunnel clearly paid off.
From the off the Red Devils were much improved with half-time substitute Marcus Rashford giving them more balance in the forward line and a direct, pacy threat down the left-hand side.
Palace were camped in their third of the field as United got higher and higher up the pitch, lobbing balls into the box and putting the Eagles' back four under increasing pressure as time went on.
Once Smalling pulled one back for the visitors they stepped it up another gear. When Lukaku equalised with 14 minutes remaining it felt like a case of when, rather than if, the winner would come.
Mourinho, of course, has form for this. The Portuguese has taken a pounding in the press in his almost two seasons at Old Trafford. But he has always been bold with his substitutions and for all the criticism which can – justifiably – be levelled at him, he has a proven track record for changing games with his substitutions. This was just the latest occasion.
When will Pogba learn?
Mourinho is a pretty simple creature. The Portuguese values discipline, sacrifice for the team and following his meticulous instructions above all else.
Making back-to-back Premier League starts for the first time since January, Pogba was stationed on the left of a midfield three – his preferred position.
The French international clearly felt he needed to make an impression and set the tone for a frustrating performance early on.
It was Pogba's misplaced pass which allowed Palace to regain possession and score the opener. Having clearly failed to learn his lesson, Pogba continued to spray unnecessary Hollywood passes around the field, usually without success.
In spite of that he still finished the game having completed 51 of the 59 passes he attempted – more than any other player on the field. That improvement can be put down to the fact he appeared to learn his lesson in the second half.
Sánchez still yet to find United role
In mitigation, Pogba's cause was not helped by Alexis Sánchez. The Chilean is yet to nail down a starting role to call his own since his January switch from Arsenal and started, nominally at least, on the left of a front three.
But instead of running at rookie right-back Aaron Wan-Bissaka the former Barcelona forward elected to come inside. Time and time again.
Quite apart from the fact it meant running into traffic all too frequently – giving the ball away an astonishing 19 times in the first half alone – Sánchez's insistence on trying to do it all himself restricted what Pogba could do.
United's No.7 was effectively playing in the space Pogba should have been occupying, forcing the Frenchman to drop deeper, as you can see from the duo's heatmaps (below), via WhoScored.
And when Sánchez wasn't getting in Pogba's way he was displaying a complete lack of commitment to the team shape, popping up on the right and attempting to dictate proceedings from there instead.
Is it really a coincidence United's two biggest signings of recent windows, marquee additions made as much for who they were rather than what they'd bring to Old Trafford, have struggled to show their worth?
Hennessey not a keeper for Palace
After succeeding Frank de Boer, Hodgson made a goalkeeper his priority in the January transfer window. But when a deal for Getafe's Vicente Guaita fell through late on the Eagles were left without an alternative.
With Julian Speroni sidelined by a knee injury Hodgson signed former Liverpool back-up Diego Cavalieri on a short-term deal until the end of the season. The 35-year-old is unlikely to get a game but Hennessey is on borrowed time at Selhurst Park.
In the first half he let a cross slip through his hands and that was a warning of what was to come.
After the restart he ambitiously came for a corner he was never going to win, missing the ball completely. Luckily for the Welsh international, Smalling headed over the open goal.
More to Benteke than goals
The big Belgian has not been prolific since his Aston Villa days. A big-money flop at Liverpool, Christian Benteke has endured a hard season at Selhurst Park with just two Premier League goals and a high-profile penalty miss to his name this term.
However, against United he was a force to be reckoned with once more – but not as you might expect. There's leading from the front as a striker . . . and then there's leading from the back.
The 27-year-old put in a sterling defensive shift for the hosts with the highlight his miraculous goal-line clearance in the second half as Mourinho's men piled on the pressure.
He won three defensive aerial duels – more than any other Palace player – typifying a warrior-like performance.
There was more to Benteke's performance than that, though. He got the assist for Townsend's goal and made a nuisance of himself against the far-from-convincing Lindelöf, winning a further four attacking aerial duels.
In the battle of the hulking Belgian strikers Lukaku got the headlines, but Benteke showed he is a valuable component in this Palace side. Now to add some goals.