Paul Heffernan fired Rovers into a deserved first-half lead with his fifth goal in six games, but the home side was unable to hold on.
Oldham Athletic substitute Jason Jarrett hit back early in the second-half to deny Doncaster their fifth successive home victory.
The result was about right on the balance of play, although Doncaster were unlucky when they hit the post seven minutes from time and also had a clear-cut penalty appeal rejected.
Oldham were first out of the blocks and could have snatched the lead straight from the kick-off.
Matt Wolfenden raced through on the left and dribbled past defender Matt Mills and keeper Neil Sullivan, but his shot lacked pace and was cleared away from the goalmouth.
Matthew Mills had a bullet-like header cleared off the line by Stefan Stam in the fourth minute and James Coppinger had a low shot tipped round the post by Richard O'Donnell, before Rovers snatched the lead in the 37th minute.
Hefernan smashed a volley into the roof of the net after Mark McCammon had headed the ball down.
Jarrett's equaliser came seven minutes after the interval when he latched on to a clearance following a free-kick to send a well-directed left-foot volley beyond the unsighted Neil Sullivan.
Visiting skipper Neal Eardley headed off the line from Adam Lockwood in the 57th minute following a corner and Rovers were denied a penalty following what looked like a blatant handball by David Livermore two minutes later.
The home side continued to pile on the pressure in the closing stages and substitute James Hayter was unlucky to see a header hit the post in the 83rd minute, before Paul Green flashed a shot inches wide from an acute angle in injury time.