Goals from Jonson Clarke-Harris and Jose Baxter ensured the honours finished even at Bramall Lane.
Clarke-Harris fired Oldham ahead during the early exchanges before Baxter, who left Boundary Park earlier this year, equalised with a spectacular set-piece.
Chris Porter and substitute Ryan Flynn both went close to claiming maximum points for the Blades, now unbeaten in seven games, near the end but neither could muster a decisive touch.
Clarke-Harris, a summer signing from League One rivals Peterborough, ensured the Blades' afternoon got off to the worst possible start when he headed home Adam Rooney's centre with only six minutes on the clock.
A comedy of errors, which saw both Harry Maguire and Shaun Miller squander possession, contributed to the hosts' demise, but the Oldham centre-forward took his chance in clinical fashion by stooping to convert from close range.
United's afternoon went from bad to worse when Aidy White, whose loan from Leeds is scheduled to expire next month, hobbled off injured while only an assistant referee's flag denied Clarke-Harris his second of the contest after George Long could only parry Korey Smith's long-range effort.
Porter, like Baxter a former Oldham player, enjoyed two good opportunities as United finally discovered their rhythm towards the end of the half.
But it was Baxter who dragged the hosts back on level terms soon after the re-start with a thunderous 30-yard free-kick following Genseric Kusunga's foul on Porter.
Only the width of a post prevented Baxter from snatching what would have been a dramatic late winner, while Porter was also agonisingly close to prodding home as the loose ball bounced around the area seconds before the final whistle.