Dele Alli was on hand to stab home a loose ball in the 87th minute after home goalkeeper Mark Howard had parried substitute Danny Green's free-kick.
Prior to the goal, Nigel Clough's side had created more chances and had the ball in the net through Mark McNulty with 15 minutes remaining, but the effort was ruled out for offside.
It was not all positive for MK Dons, though, as they ended the game with 10 men when Green was shown a second yellow in the dying moments for a clumsy challenge.
The win means Karl Robinson's side are now unbeaten in nine league games and are up to third in the table, a point behind Swindon and two behind Bristol City, with a game in hand on both.
Sheffield United remain in fifth on 31 points, six points behind the Dons.
Tuesday's other League One fixture also took place in south Yorkshire, with Doncaster Rovers claiming a 1-1 draw at local rivals Barnsley.
The visitors were forced to come from behind after Lewin Nyatanga headed the home side in front in just the fifth minute.
Theo Robinson's strike from inside the box seven minutes after half-time gave Paul Dickov's side a share of the spoils at Oakwell.
The result means the two remain level on 23 points, with Barnsley two places ahead of Doncaster in the table in 14th courtesy of a superior goal difference.
