Promotion-chasing Rovers had John Marquis sent off for two bookable offences after 51 minutes.
Steve Seddon then put the Dons ahead on 67 minutes with substitute Shane McLoughlin sealing a first league home win since Boxing Day in injury time.
Wally Downes' side are now seven points from safety, while Rovers remain sixth despite a fifth game without a win.
The game was 20 minutes old before Toby Sibbick's fierce drive forced Rovers keeper Marko Marosi into the first save of the game.
But the Dons right-wing back then failed to hit the target after Michael Folivi's jinking run and pass had sent him clear.
Marquis headed Rovers' best chance of the first half onto the top of the bar following James Coppinger's 37th-minute free-kick.
It was the Rovers striker's last positive contribution as he was booked for tangling with Simon Wagstaff just before half-time.
Marquis received his marching orders just seconds after Aaron Ramsdale tipped over Ben Whiteman's 20-yard shot which looked bound for the top corner.
After Ramsdale saved Butler's header from the resulting corner he was blocked by Marquis who was shown his second yellow card.
The 10 men held out until Joe Pigott's pass allowed Seddon to blast a left-foot shot past Marosi.
Ramsdale twice denied Coppinger on the closing stages before sub McLoughlin sealed the points with a low right-foot shot in injury time.