Home skipper Adam Murray's seventh-minute free-kick was all they needed in the end, though Jamie McGuire had to clear an Alan Bennett effort off the line 11 minutes from time.
The afternoon began with injury woes for the Dons and that early Mansfield goal.
The visitors were down to 10 men as George Francomb was getting attention for a head wound when the Stags went ahead after seven minutes.
Murray lashed in a free-kick from 30 yards which Ollie Palmer tried to get a head on. The striker failed to get a touch but his attempt was enough to put off keeper Ross Worner as the ball sailed past the pair of them into the net.
The Dons were then forced into a 15th-minute change when Darren Jones was stretchered off after taking a high boot from Anthony Howell in the face.
The visitors rarely threatened the home goal though might have levelled on 42 minutes had Kwesi Appiah caught his half-volley with more power from Francomb's cross.
Francomb should have levelled four minutes into the second half when Appiah's cross cued him up for a volley seven yards from goal at the far post only to slice it over.
A half of few chances saw the Dons finish strongly and 11 minutes from time Jamie McGuire kicked an Alan Bennett header off the line from a corner with Alan Marriott beaten.