But Doncaster were left kicking themselves because they should have had the points sewn up and only had themselves to blame for not leap-frogging above their opponents in the table.
Rovers made a whirlwind start and dominated for large periods of the first half after snatching the lead in the fifth minute.
James Hayter rammed home from close range after good work from John Oster and James Coppinger but Rovers went on to miss a couple of golden opportunities to put the game out of sight.
Shelton Martis fired wide from only two yards out after latching on to a cross from Oster in the 16th minute and Hayter headed wide at an open goal five minutes later.
United's only first-half threat came from tricky winger Henri Camara who delivered a raking cross in the 13th minute which should have led to a goal but Richard Cresswell just failed to connect with a diving header attempt at the far post.
Hayter had another fierce effort tipped around the post by on-loan keeper Steve Simonsen and Doncaster continued to force the pace at the start of the second half.
Coppinger had a goal-bound shot blocked after cutting inside in the 53rd minute and Martin Woods saw a cracking 20-yarder tipped around the post by Simonsen 15 minutes later.
But the home side began to look nervous when United started to press forward and the Blades were unlucky not to be awarded a penalty when Martis appeared to push Cresswell in the back.
Rovers seemed to have weathered the storm but United's persistence was rewarded when Harper scored with a deflected shot from just inside the box two minutes from time.
Rovers still had a chance to pinch a winner in the third minute of stoppage time but Hayter blazed high over the bar with only the keeper to beat.