Early goals from Daniel Powell and Peter Leven lifted the Dons up to eighth in League One and condemned Rovers caretaker boss Darren Patterson to defeat in his first game in charge.
Milton Keynes were rampant in the first half and Jabo Ibehre hit a post before Powell opened the scoring in the 10th minute, blasting a swerving 20-yard shot past Mikkel Andersen.
Leven doubled the lead three minutes later when his deflected 25-yard free-kick wrong-footed Andersen, after Byron Anthony had hauled back Ibehre.
Powell then had a goal ruled out for offside before Ibehre fizzed a diving header just over the bar, while Will Hoskins and Chris Lines tested Dons keeper David Martin from distance.
The Dons pressed for a third goal late on but Andersen saved well from Leven, Michael McIndoe and substitute Sam Baldock, who also curled a shot against the post.