Rovers led through a Kelvin Mellor own goal and a stunning Harrison Biggins strike but were pegged back by Shaun Whalley and Seamus Conneely.
Doncaster made an impressive start count after nine minutes. Mo Faal sent a header bouncing off the crossbar, with the ball falling to George Broadbent, whose driven effort ricocheted in off Accrington’s Mellor.
Despite excellent opportunities for Faal and Luke Molyneux, Rovers could not extend their advantage.
Accrington looked to have equalised after 72 minutes when Josh Andrews fired home but, after the goal was initially given, it was overturned by referee Ross Joyce.
The visitors did find the leveller two minutes later when Whalley curled home an excellent finish from the edge of the box.
Biggins netted with a piledriver from 30 yards in the 81st minute to restore Rovers’ advantage, but a replay was set when Conneely sidefooted home a low corner at the near post five minutes from time.