Ex-Oldham striker Chris Porter hit a late equaliser for the Blades, cancelling out a first league goal by Wales defender James Wilson.
Oldham snatched the lead after 17 minutes when Connor Brown’s right-wing cross was headed firmly into the bottom corner from eight yards by Wilson.
Jonson Clarke-Harris fired just off target for the home side and United’s Stefan Scougall curled a shot inches wide after neat footwork inside the box.
The visitors missed a glorious chance after 33 minutes as Jose Baxter pounced on a defensive error and went clean through on goal only to be denied by keeper Paul Rachubka.
Oldham defended well under growing pressure and they also had a slice of luck midway through the second half when Blades defender Terry Kennedy headed against the bar.
United grabbed their equaliser six minutes from time when substitute Porter slotted home from four yards after superb play down the right by Jamie Murphy.
United are unbeaten in seven games while it’s now nine without defeat for the Latics.