Milton Keynes took the lead after just over a minute of play. Luke Chadwick had his shot saved by Lucas, only for the ball to fall to Wilbraham who couldn't miss from close range.
Both Paynter and Douglas hit the post and bar for Swindon in the first half.
However Milton Keynes doubled their lead on 37 minutes when James Tunnicliffe was left unmarked and scored with a close range header after a MK Dons corner.
Late into the second time Swindon pulled a goal back with a powerful shot from Danny Ward making it 2-1 deep into injury time.
Overall Swindon were unluckly not to have at least taken a point from the game. This defeat leaves Swindon in 6th place going into Saturday's away trip to Brighton.