The Blades went 1-0 and then 2-1 down in the first half before a stunning second-half fightback saw them close the gap between themselves and leaders Burnley, with Oli McBurnie on the scoresheet twice.
Jack Robinson also scored, to redeem himself after his error led to Burnley’s second, with Anel Ahmedhodzic and Iliman Ndiaye also on target.
Here’s how we rated the Blades’ players on a five-star afternoon at Bramall Lane...
1. Wes Foderingham 8
Could do nothing at all about the two goals he conceded and then sat back and had the best view in the house as United ran rampant in the second half. Made a smart save from Harwood-Bellis as time ticked down and Burnley looked to get back into the game Photo: Ashley Crowden
2. George Baldock 7.5
Could have got in on the action himself when he got on the end of Norwood's through-ball and went one-on-one with Muric, but the goalkeeper saved and McBurnie was there to tap in the rebound. Went down for some treatment late in the game but soldiered on before being replaced late on Photo: Bradley Collyer
3. Anel Ahmedhodzic 8.5
Came straight back into the side at right centre-half after his suspension, with Chris Basham dropping to the bench. Got a nasty whack in the second half from Cullen but with Bramall Lane baying for a red, ref Bond showed a yellow. Good assist for McBurnie's goal and got one himself later with a great finish. Photo: Andrew Yates
4. John Egan 8
The man holding it together in the middle amidst all the chaos, for the most part. Defensively solid although he looked to be in some pain late in the game as he limped around - United don't need him to become their latest injury victim Photo: Simon Bellis