The Old Trafford side had seen their position in the league overtaken by Manchester City on Tuesday. Looking to climb back atop the table, they were undone by goals from Kean Bryan and Oliver Burke, which came on either side of a Harry Maguire strike in the second half.
The loss keeps Ole Gunnar Solskjaer’s men on 40 points from 20 matches, one point behind City who also have a game in hand.
Sheffield United went in front after 24 minutes, when Bryan guided his header from the centre of the box past David de Gea after a corner kick.
But Burke completed the upset 10 minutes later when his shot from inside the box deflected off Man United centre-back Axel Tuanzebe and beat De Gea who was diving the other way.