Lys Mousset outmuscled a calamitous Phil Jones to help set up the opener, as John Fleck bundled home.
And Fleck then turned provider, sliding in Mousset in the second half, with the Frenchman rushing clear before converting low into the right corner. United had hope when Brandon Williams halved the deficit with a brilliant low volley before fellow teenager Mason Greenwood equalised soon after coming on.
In a breathless seven minutes, Marcus Rashford then put United ahead but a late twist saw Oliver McBurnie hit a third to salvage a draw after a VAR review.
Here are the player ratings from Bramall Lane.
Player ratings: Sheffield United vs Manchester United
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