Mildenhall denied Jack Midson on three occasions while Rovers felt they should have had a penalty when Matt Harold went down but the Pirates rarely threatened.
After a lifeless 40 minutes Midson got on the end of Harry Pell's long ball before rounding Mildenhall.
Midson dallied however and Mildenhall scrambled back to save before the Dons' Crystal Palace loanee Kwesi Appiah headed narrowly over before hitting a dipping volley from 20 yards just over the bar.
Soon after the break Midson ran at the Rovers defence and shot from 20 yards, but Mildenhall tipped the ball over for a corner.
In the 75th minute Wimbledon twice came close to scoring. First Mildenhall superbly denied Midson from close range then substitute Kevin Sainte-Luce set up George Francomb but Lee Brown blocked his goal-bound effort.
The visitors then had a strong shout for a penalty turned down when Harrold was dragged down by Darren Jones but neither side could break the deadlock and both edged closer to safety.