The winning goal came early on as Lyle Taylor converted Tom Elliott's rebounded effort for his 21st goal of the season.
Taylor was then denied by Orient keeper Alex Cisak, before Cisak was on hand again to punch away Elliott's effort.
Seventh-placed Wimbledon now need two points from their final three games to seal a play-off spot.
AFC Wimbledon strengthened their League Two play-off chances with a narrow home victory over Leyton Orient.