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Under-pressure boss Michael Carrick saw his side go 2-0 down inside four minutes but they fought back to level before half-time only to disintegrate defensively again early in the second half. Many had departed when they launched their latest improbable comeback.
Joshua Zirkzee swept in what looked like a consolation goal in the 92nd minute and when Zion Suzuki flapped at one final corner, Patrick Dorgu headed into the net to stun Villa. United still have not won a Premier League game since August but it was Unai Emery fuming.
Villa were rampant at the start, Alysson beating Senne Lammens on the angle inside a minute before the same player's shot proved too hot for the goalkeeper to handle and presented Nicolas Jackson with the chance to put United two down after four minutes.
That was the earliest that United had been two down in a Premier League game but Old Trafford only had to look to Tuesday - and their 3-2 victory over Roma - to recognise that being two behind need not be fatal to their hopes. Momentum did turn in their favour.
Matheus Cunha drew a penalty when Boubacar Kamara lunged in and Bruno Fernandes converted. Suzuki's goal was peppered thereafter, the chants from the Stretford End against the ownership briefly subsiding as United pushed for a deserved equaliser.
Youri Tielemans found it against his former club before the interval and United looked narrow favourites at the break. But another calamitous start to a half undermined them, Diogo Dalot bringing down Alysson for John McGinn to score from the penalty spot.
When Leny Yoro headed towards his own goal soon after and Lammens could only push it against the post, Jackson miskicked before Leon Goretzka forced the ball home to restore Villa's two-goal advantage. United's lamentable defending is a massive issue.
At that stage, there could be no confidence that a defence that has now conceded more goals than any other in Europe's major leagues in all competitions would not let in a fifth but, instead of it petering out, Zirkzee and Dorgu came off the bench to do the unthinkable.
The point still lifts Villa into the top half of the table but feels like two dropped. As for United - this chaotic, confusing United - they are in the relegation zone after 10 games. A club at odds with its fans, running on fumes, but still capable of two comebacks in one game.
Skysports