Jake Edwards put the Grecians ahead with a close-range strike midway through the first half and teenager Dean Moxey made sure with a header three minutes into the second period.
Exeter created a host of chances and were denied by a string of fine saves from Rovers' keeper Steve Perrin.
Rovers gave Exeter an early scare when former Grecian Jon Richardson floated a free-kick inside the box and striker Kevin Rapley, making his debut on-loan from Chester, drilled a low shot past the post in the second minute.
Two minutes later Les Afful went close for the Grecians when he lobbed Rovers goalkeeper Perrin but saw his effort scrambled off the line by Des Lyttle.
The visitors had their best moments early in the half. Adam Garner was left unmarked from Jon Beswetherick's corner and, when his header was blocked, Charlie Griffin struck a close range shot over the bar.
Exeter eventually went ahead midway through the half. Afful shook off defender Darren Davies and his fine low cross was tapped home at the far post by Edwards.
Exeter controlled the first half and created enough chances to put the game beyond the visitors.
But they were denied by a string of fine saves by Perrin who kept out strikes from Sean Devine and Alex Jeannin.
After the break Exeter took just three minutes to grab a second. Jeannin's corner was met by Moxey and the teenager's header flew past Perrin and into the top corner.
Rovers attempted to respond and Damon Searle forced Paul Jones to save well with a looping shot from 30 yards.
Perrin again saved well to keep out Jeannin as Exeter looked certain to increase the scoring further.
Rovers ended the game strongly and Griffin should have pulled a goal back when he headed Mark Danks' cross over the bar.
But there was no way back and Exeter were good value for the three points.