Jon-Paul McGovern's superb 40-yard lob for the Robins – who were thrashed 5-0 at Gillingham on Saturday - was cancelled out by Jermaine Easter's 53rd minute penalty for the Dons.
But Paynter's double and David McCracken's own goal condemned Dons boss Paul Ince to his first defeat since returning to stadium:mk.
Swindon dominated the first half and Lloyd Macklin gave the hosts an early scare when he beat stranded Dons goalkeeper Willy Gueret to a long ball but failed to pick out a team-mate from the by-line with the net gaping.
Michael Timlin twice went close for the Robins, first when his curling 20-yard free-kick was well saved by Gueret and then when his long-range half-volley flew inches wide.
And McGovern produced a moment of magic against his old club to deservedly put Swindon ahead four minutes before the break.
Gueret raced out of his box to head away a long ball and, with the Dons' stopper still out of position, McGovern launched an audacious 40-yard half-volley back over his head and into the net.
Milton Keynes burst out of the blocks after the interval and Easter opened his account to equalise with a cool 53rd minute penalty, after Lewis Gobern had been tripped in the box by Lescinel Jean-Francois.
But Swindon restored their lead just three minutes later as Paynter's fierce left-foot shot from the edge of the box took a deflection off Dons defender Mathias Doumbe and flew into the corner of the net.
Paynter completed his brace to make it 3-1 in the 71st minute, poking the ball home from a yard after the jittery Gueret had dropped Anthony McNamee's routine cross.
And McCracken's own goal three minutes later sealed the rout as he headed Macklin's dangerous cross past Gueret under pressure from Paynter at the far post.