The win means Dons likely need just a point from next weekend's game against Walsall to enjoy home advantage in the second leg of their play-off semi-final against Huddersfield.
The visitors took the lead three minutes in when Luke Chadwick robbed Gary Jones of possession on halfway and raced towards the penalty area. He slipped a pass to Jay O'Shea, who drifted by Stephen Darby and fired a low drive through goalkeeper Matt Edwards' legs.
O'Shea clipped the crossbar later in the first half after being teed up by Stephen Gleeson but Dons stopper David Martin was the busier for much of the half. Dale's best chance fell to Joe Thompson, who should have done better when O'Shea's wayward pass sent him through on goal but his weak shot was comfortably saved.
Michael Symes worked Martin with a header early in the second half but Karl Robinson's side doubled their advantage in the 57th minute to make the result safe. Jabo Ibehre's clever backheel sent O'Shea running towards goal and he picked out a pass for substitute Dean Bowditch, who stroked past Edwards with his first touch of the game.
Jean-Louis Akpa Akpro pulled one back for the hosts late on but the visitors' lead was never under threat.