Mark Yeates equalised for Sheffield United four minutes into injury time after Burnley looked to have snatched all three points at Bramall Lane.
Dean Marney's header gave the visitors the lead and Chris Eagles made it 2-0 from the penalty spot.
Daniel Bogdanovic raced clear to pull one back and Ched Evans made it 2-2 from Yeates' cut-back.
Jay Rodriguez's 90th-minute strike looked to have won it for the visitors only for Yeates to fire in a low shot.
The Blades made a bright start, almost taking the lead inside the opening five minutes when Bogdanovic was set free down the left and squared to Johnny Ertl, whose thumping effort from the edge of the area was tipped over by Burnley keeper Brian Jensen.
Burnley should have gone ahead just before the half-hour but Andre Bikey headed over from three yards following Daniel Fox's corner.
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