Man United manager Ole Gunnar Solskjaer rotated the team after the win over Liverpool in the FA Cup, as Axel Tuanzebe and Alex Telles both got rare starts alongside the return of goalkeeper David De Gea, Bruno Fernandes, Anthony Martial and Nemanja Matic.
After the hosts failed tomake their early dominance count, the Blades opened the scoring in the 23rd minute after Kean Bryan rose the highest at the near post to guide his header in off the post..
The Red Devils thought they had equalised from a corner situation on the half-hour mark after shot-stopper Aaron Ramsdale spilled a cross under pressure from Harry Maguire, with Martial scoring from the rebound but the goal was disallowed for a foul.
Solskajer's charges were probing to get back into the game in the closing phase of the first stanza but they were kept at bay the Sheffield defence and the visitors went to the break leading by an odd goal.
With Man United coming out to attack in the second half, Maguire finally equalised for the Red Devils in the 64th minute with a header into the bottom corner after a corner by Telles.
Man United were punished in the last quarter of an hour after Martial lost possession, allowing the Blades to break on the counter, which ended with Oliver Burke restoring their lead with a powerful effort that deflected off the thigh of Tuanzebe and sailed into the back of the net.
Even with the introduction of Luke Shaw and Donny van de Beek late on, Sheffield managed to keep the hosts at bay and clinched only their second win of the season while Man United remain a point behind leaders Manchester City, who have a game in hand.