The Blades midfielder, recalled to the side in place of Darius Henderson, lashed a low, right-footed shot into the bottom corner from the edge of the penalty area in the 88th minute.
James Hayter had fired Doncaster into a fifth-minute lead and it appeared Rovers were set to leapfrog their neighbours into seventh place before United were rewarded for a stirring late fightback after being outplayed for much of the match.
Kevin Blackwell's United side won for the first time in four league encounters when they claimed a welcome 3-0 victory over Blackpool in midweek, but despite Harper's late equaliser they are still chasing their first away success in the Championship since early December.
Although victory was snatched from them, Doncaster stretched their unbeaten league run to six matches and remain in eighth place, a point behind United.
United manager Blackwell handed a debut to Stoke goalkeeper Steve Simonsen, signed on loan on Friday, and brought Harper back.
Doncaster trio James O'Connor, Mark Wilson and Hayter all returned to O'Driscoll's starting line-up, with the latter wasting little time in seizing his chance after stepping in for leading goalscorer Billy Sharp, who was left out against his parent club.
The hosts made their early breakthrough when midfielder Wilson crossed from the left and Hayter steered the ball into the bottom corner from six yards for his seventh goal of the season.
United striker Richard Cresswell headed over the crossbar, before the Wilson-Hayter combination at the other end again opened up the visitors, but this time the goalscorer dragged his shot wide.
Simonsen then earned his spurs for the Blades, diving at full stretch to turn away another effort from Hayter, who had pounced on James Chambers' cross to steer the ball goalwards.
Blades defender Marcel Seip blocked James Coppinger's shot from inside the penalty area early in the second half as Doncaster looked to pick up where they had left off at the end of the first period.
But substitute Glen Little, a half-time replacement for Mark Yeates, fired a left-footed shot straight at Doncaster goalkeeper Neil Sullivan as the visitors wrestled back an even share of possession.
Doncaster midfielder Jay Emmanuel-Thomas, on loan from Arsenal, was off target when he tried his luck from 20 yards, but Martin Woods forced Simonsen into another impressive save in the 70th minute with a left-footed drive as Rovers passed their way back into the ascendancy.
Hayter thumped a 30-yard effort which was well held by Simonsen before the visitors ventured forward to go close with two headers, the first from Kyle Bartley flying over the crossbar and the second, from Cresswell, gratefully gathered by Doncaster goalkeeper Neil Sullivan.
United sensed they could salvage a point in the closing stages as Harper rifled a right-footed shot just off target.
And Blackwell's side snatched a point in the 88th minute when Andy Taylor, a second-half replacement for Henri Camara, crossed to the edge of the penalty area from the left and Harper fired the ball home into the bottom corner.