In a game of two halves, Sheffield United took a two-goal lead but Manchester United rallied back to edge in front before allowing the Blades back into the game.
Manchester United are now 9th on 17 points while Sheffield are sixth with 18 points.
David de Gea was called into action in the 12th minute to produce two remarkable double saves; first the Spaniard dived to his right to palm away John Lundstram’s shot from range before diving to his right just seconds later to block David McGoldrick’s goal-bound header.
There was little De Gea could do seven minutes later when he blocked Lundstram’s shot with the ball rebounding off John Fleck into the net for the opening goal of the game.
After the break, the visitors lost the ball in a dangerous position and Sheffield made them pay when Fleck fed Lys Mousset and the French striker wandered forward before striking a low effort beyond the reach of De Gea in the 52nd minute.
Manchester United then launched one of their famous old comebacks reminiscent of the Sir Alex Ferguson era in a seven-minute spell.
The hosts could only half-clear Daniel James’ cross from the right and academy graduate Brandon Williams half-volleyed the dropping ball into goalkeeper Simon Moore’s left-hand corner in the 72nd minute.
Substitute Mason Greenwood found the equalizer with his first Premier League goal five minutes later when he tucked in Marcus Rashford’s cross into the six-yard box.
Good interplay between the Red Devils’ forwards ended up with James squaring for Rashford to finish into an unguarded net in the 79th minute.
The hosts were not prepared to give up just yet and in the 90th minute substitute Oliver McBurnie did well not to handle Callum Robinson’s cross, before firing past De Gea to nick a point for Chris Wilder’s men.