Bruno Fernandes missed a 93rd-minute penalty as Aston Villa won at Old Trafford for the first time in 12 years in a pulsating match.
Kortney Hause had put Villa ahead with a powerful header two minutes from the end of normal time before the defender handled inside the box to present United with a lifeline.
However, Fernandes blazed high over the bar in front of the Stretford End as United’s unbeaten start to the Premier League season came to an end.
Having suffered an early Carabao Cup exit at home to West Ham, United have lost their past two games without scoring.
Villa missed two big chances before a dramatic finale.
After Matt Targett blazed over inside the six-yard area, Ollie Watkins could only fire at David de Gea after the United keeper had passed straight to the Villa forward following Harry Maguire’s backpass.
In a thrilling game, Ezri Konsa also headed another chance over after beating Aaron Wan-Bissaka in the air, while Watkins was denied by De Gea at full stretch in the second half.
At the other end, Emiliano Martinez kept out Maguire’s header and Paul Pogba nodded wide when the France midfielder should have scored.