Jack Payne’s penalty eased the pressure on Bradford City with a first win for head coach David Hopkin.
The substitute fired home on the stroke of half-time to earn a first victory since August 21.
The result lifted City out of the bottom four as their defensive doggedness made it back-to-back clean sheets.
With Eoin Doyle ruled out by a back injury, Kai Bruenker was promoted for his first start of the season alongside George Miller.
Midfielder Jim O’Brien added to City’s lengthy casualty list when he limped off with a hamstring problem after half an hour of frantic but featureless action. But Wimbledon were almost gifted an opening goal when Richard O’Donnell misjudged a long ball, which he allowed to bounce over his head. With the goalkeeper on the ground, Joe Pigott only had to knock the ball into the empty goal, but missed from five yards.
City took the lead against the run of play in the 45th minute after Miller was brought down by Deji Oshilaja, Payne sending Joe McDonnell the wrong way from the spot.
Wimbledon pushed for an equaliser and Anthony O’Connor produced a superb goalline clearance to keep out a header from Jake Jervis.
Wimbledon: McDonnell, Watson (Appiah, 66), Oshilaja, McDonald, Purrington, Wagstaff, Trotter (Wordsworth, 73), Soares, Pinnock (Barcham, 73), Pigott, Jervis. Unused substitutes: Nightingale, Hartigan, Garratt, King.
Bradford City: O’Donnell, Mellor, McGowan, O’Connor, Knight-Percival, Scannell, L O’Brien, J O’Brien (Payne, 30), Wood, Miller (Isherwood, 89), Bruenker (Ball, 69). Subs not used: Gibson, Goldthorp, Staunton, Sykes-Kenworthy.
Referee: Keith Stroud.