A second-half strike from Gareth Sheldon was enough to give Exeter their first win under new boss Neil McNab.
Rovers started brightly and Rob Quinn headed Adam Barretts corner just over the bar in the fourth minute.
Steve Flack had ExeterÂ’s best early moment when he rose well to meet James CoppingerÂ’s cross but he headed the ball over the bar.
David Lee almost put Rovers ahead when his shot beat the goalkeeper but was denied by Scott Hileys clearance off the line.
Lewis Hogg should have put Rovers ahead just after the break when he met Mark McKeeverÂ’s low cross but his shot from close range was superbly blocked by Kevin Miller.
Exeter won the game in the 66th minute when CoppingerÂ’s cross eluded the Rovers defence and Sheldon volleyed home from close range.