Nigel Clough’s play-off chasers were behind to a double from Dominic Poleon but goals from Jason Holt and Jamie Murphy extended their unbeaten away run to eight games.
United wasted the first real chance as Ryan Flynn picked out Marc McNulty, whose shot was blocked by the feet of goalkeeper Joel Coleman
Oldham took the lead after 22 minutes when Poleon seized on hesitation in the visiting defence and charged into the box before driving his 12-yard shot into the far corner of the net.
Poleon’s second goal, in the 43rd minute, was an absolute stunner as he turned 35 yards out and unleashed a thunderbolt of a strike past United keeper Mark Howard.
Poleon almost got his hat-trick goal after the break but United pulled one back in the 56th minute when Oldham failed to clear a Paul Coutts cross and Holt swept the ball home from eight yards.
The Blades bagged a controversial leveller after 73 minutes when referee Richard Clark over-ruled his assistant to give them a corner and, following a goalmouth scramble, Murphy forced home from close range.
Clough’s side pushed for a winner and nearly got it but Michael Doyle saw his 20-yard shot come back off a post.