It had looked like the Dons would have to settle for a point after Samir Carruthers' equaliser, but Reeves' late intervention has lifted them to within seven points of sixth-placed Peterborough.
Oldham took the lead after 37 minutes when Gary Harkins' chipped cross from the left was flicked into the far corner by the head of Adam Lockwood.
Carruthers gave his side the lift they needed early in the second half when he rode two challenges and side-stepped a third before finishing into the bottom corner.
Reeves then came within a whisker of putting the Dons ahead when his low shot from the edge of the penalty area came back off the far post.
The Latics were reduced to 10 men when Genseric Kusunga was shown a second yellow card and they just failed to hold out as Mark Oxley pushed Carruthers' cross into the path of Reeves, who tapped into an empty net.
- Sports & Recreation
- Samir Carruthers
- Gary Harkins