The Clarets were unbeaten in 17 games going in to the tie, but a seven goal thriller at Bramall Lane saw Vincent Kompany's side suffer their first defeat since their 1-0 loss to Watford in August.
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The home side had gone 1-0 down to the table toppers thanks to Claret's star Manuel Benson.
Iliman Ndiaye brought the Blades level, but Benson was soon at it again, regaining the lead for Vincent Kompany's side just before half-time.
But after the restart, Paul Heckingbottom's side sprung into life.
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Long-standing fan favourite Oli McBurnie fired his side back level just after the break, before Jack Robinson - who played an unfortunate role in Burnley's opener after heading Benson's goal-bound shot into his own net - put his side in front.
By this point, the visitor's defence looked defeated, as Anel Ahmedhodzic and McBurnie each netted to put the Blades 5-2 up by the 74th minute.
"Wow, wow, wow," talkSPORT's GameDay presenter for the match Dan Windle said after the final whistle, "That was absolutely absorbing."
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Ex-Burnley striker Chris Iwelumo joined Adam Bridge to commentate on the Championship clash, and the former Clarets man gave an honest assessment of his old club's second half collapse.
"They got the first goal after halftime and Burnley were rocked," he said, "They never reacted to it."
He continued: "Burnley are allowed a defeat. The performance level dipped but they can't do it again, nip it in the bud straight away and get back to winning ways, it's a simple message.
"They'll be hurting like they've not hurt before in the dressing room. The players know exactly what the Championship can do. They got beaten up today. Beaten up, massively."
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The Blades' win sees them go just three points off the Clarets at the top of the Championship as Kompany suffered only his second defeat since he arrived at Turf Moor.
Burnley next face bitter rivals and third place Blackburn next week, with both Lancashire teams fighting for the Championship top spot.