A mistake by Exeter full-back Craig Woodman gave Dave Clarkson an opportunity after just five minutes and the striker made no mistake to notch his second goal since joining the club from Bristol City with a well-placed shot into the corner.
Former Rovers striker Jamie Cureton missed a great chance to equalise for Exeter when he went one on one with Neil Etheridge, but the goalkeeper saved well as the veteran frontman tried to round him.
Exeter levelled on the stroke of half-time when Cureton received Matt Oakley's pass with his back to goal and swivelled superbly before slotting in his seventh goal of the campaign.
The Grecians looked set to go on and win as they bossed the second half, but they could not turn possession into goals.
That came back to haunt them as goalkeeper Artur Krysiak allowed a soft shot by striker Elliot Richards to slip through his hands at his near post on 69 minutes for Rovers to get their maiden win.