Rovers came closest to scoring in the first half when Byron Anthony let fly from 35 yards but his shot cannoned back off the underside of the crossbar before being cleared to safety.
Adam Stansfield missed two good chances for Exeter, the best of which a shot that went wide of goal from 10 yards, which he really should have done better with.
After the break, chances were few and far between. Exeter's best effort was from Richard Duffy, whose long range shot had to be tipped over the bar by Mikkel Andersen, while Paul Jones saved well from Chris Lines at the other end.
Then, with the game looking set to end goalless, Dunne stooped to head in at the near post and seal a vital win for the Grecians.