Goals from Nick Fenton, Steve Roberts and Paul Heffernan proved enough, despite late goals from Gary Smith and Aaron Wilbraham threatening a comeback for the hosts.
Dons boss Danny Wilson made two enforced changes from the team that drew 2-2 with Huddersfield, after Clive Platt and Wade Small failed to recover from knocks picked up in the midweek clash.
Wilbraham replaced Platt up front, while Gareth Edds filled in for Small on the right of midfield.
Doncaster boss Dave Penney made two changes from the team that lost 1-0 at Gillingham in midweek with Michael McIndoe returning from a knee injury and Jonathan Forte favoured to Lewis Guy up front.
The Dons started brightly with some neat passing football but Fenton broke the deadlock for the visitors against the run of play from the first corner of the match in the 13th minute.
Sean Thornton whipped a dangerous in-swinging delivery into the six-yard box and the unmarked Fenton stole in ahead of Matt Baker to head into the gaping net.
And then just 11 minutes later Roberts evaded his marker to put Rovers 2-0 up from another corner.
Thornton curled in an in-swinger and after everyone missed it at the near post, Roberts was given space just five yards out to swivel and fire home his first goal for the club.
Forte wasted a good chance to make it 3-0 just after the half-hour mark when he scuffed a good chance straight at Baker, before Izale McLeod should have pulled a goal back for the Dons in the 37th minute.
The pacey McLeod pinched the ball off centre-half Steve Foster and raced clean through on goal, but keeper Jan Budtz spread himself well to make the save.
And then Smith curled a 30-yard free-kick just past the post after Ricky Ravenhill was booked for bringing down Stephen Quinn.
Milton Keynes started the second half purposefully and Wilbraham's header from Smith's corner was hacked off the line by Doncaster full-back Sean McDaid two minutes after the re-start.
And then McLeod turned McDaid on the edge of the box but his well directed strike was clawed out of the top corner by Budtz.
Smith's deflected long-range strike was almost turned in by the sliding McLeod in the 71st minute as the Dons continued to press, before Smith pulled a goal back for the hosts two minutes later.
Substitute Nicky Rizzo played a quick corner to Smith, whose chip into the box bounced straight into the net as keeper Budtz was put off by Wilbraham's attempted header.
Budtz saved well from Malvin Kamara in the 78th minute after the substitute had been put through on goal by Wilbraham, before Heffernan put the visitors 3-1 up in the 85th minute.
Craig Morgan played a poor back pass and Heffernan latched on to it before slotting his ninth goal of the season past Baker.
Wilbraham capitalised on substitute Sam Oji's poor back pass to ram home the Dons' second goal just a minute later, but there was to be no great escape for the hosts.