Kean Bryan and Oliver Burke scored for Sheffield, with Harry Maguire grabbing the consolation for the Red Devils.
Ole Gunnar Solskjaer made six changes to his side that defeated Liverpool in the FA cup tie on Sunday, with the likes of Axel Tuanzebe and Nemanja Matic starting.
On the other hand, Chris Wilder’s men were short on numbers in their squad with up to eight players unavailable, and could name only six substitutes on the bench.
In the first half the visitors sat deep, with Manchester United having a lion share of the ball but made no good use of it as they failed to test Aaron Ramsdale.
Sheffield United took the lead midway through the first half after David de Gea failed to deal with Kean Bryan from a Sheffield corner. The former Manchester City man became the first Blades player to score at Old Trafford in 28 years.
The visitors then took the lead once again after Oliver Burke unleashed a strike that deflected off Axel Tuanzebe, and found its way into the back of the net.
The result gives the blades hope in their race to scale up from the relegation zone whiles Manchester United are a point behind Manchester City, who have a game in hand.
Elsewhere at Turf Moor, Burnley emerged victorious with a 3-2 win over against Aston Villa, with a late goal from Chris Wood making the difference for Sean Dyche’s side.
Earlier in the evening, Thomas Tuchel’s first game in charge of Chelsea ended in a goalless draw as his new side failed to make the most of their superior possession against a spirited Wolves side at Stamford Bridge.