The Dons responded immediately and good build-up play presented a chance for Stephen Gleeson, but his shot was deflected wide for a corner.
The away side then went back up the other end but again found Martin in good form as he tipped away Nathan Byrne's right-footed shot.
However, the goal did come for Mark Cooper's side when Pritchard curled in a free kick.
The lead was almost doubled before the break but Martin made a crucial double save, first pushing away Pritchard's effort before denying Nile Ranger after the striker had made space on the edge of the box.
The turning point came soon after, however, when Nathan Byrne was shown a straight red card as he appeared to stamp on Shaun Williams.
Swindon's keeper was called into action again, this time pushing Chadwick's shot over the bar.
George Baldock thought he had found the winner for the Dons in the 89th minute but was flagged offside as he struck from a few yards out.