Karl Robinson’s side had not won since Boxing Day but completed the league double over the Blades to climb back above Preston into third place.
Former Coventry winger Baker produced the first effort of the game for the home side in the 16th minute but his left-footed strike whizzed just wide.
Baker threatened again after 42 minutes, but his powerful shot proved easy pickings for Mark Howard in the Blades’ goal.
Jamal Campbell-Ryce should have given the visitors the lead just before the break when a long clearance sailed into his path, but his poked effort was blocked by Dons goalkeeper David Martin.
Blades teenager Louis Reed threatened minutes after the restart with a fizzing shot that arrowed wide, but Baker hit the only goal in the 67th minute, surging through after good hold-up play from Will Grigg to smash home his fifth of the season.
The Dons never really looked threatened after Baker’s striker as they held on for the victory which drops the Blades out of the play-off spots on goal difference.