Grant McCann's side enjoyed almost two-thirds of possession but had to wait a long time to make that count, with Luke Molyneux scoring the only goal of the game via the penalty spot two minutes from time.
The visitors almost took an early lead when Sonny Cox somehow missed the target from just a few yards out as Rovers, with five debutants in the starting XI, were caught cold at the back.
The hosts then mounted a series of attacks themselves with wide men Glenn Middleton and Molyneux both forging chances in quick succession but they had to survive another scare just after, when Matty Pearson almost scored an own goal. The centre-half volleyed onto his own crossbar after a wicked, inswinging free-kick from Exeter's skipper Reece Cole.
Jamie Sterry then went off injured midway through the first half in a big blow for the hosts; the vice-captain suffered a hefty blow when Exeter's goalkeeper Joe Whitworth came for a cross but clattered into Sterry and one of his own players. After some treatment, the defender groggily departed the field in what was classed as a concussion substitute.
Harry Clifton saw a long-range effort go wide in the first chance after the restart before sub Robbie Gotts then blazed over as McCann's men upped the ante.
Exeter were more than content for Rovers to boss possession for virtually all the game, but still looked tidy in the rare passages of play where they did have the ball.
They seemed content to let the game play out to a natural draw but it was Rovers who were showing more intent. Tottenham loanee Damola Ajayi was denied a dream debut goal when a backtracking Exeter defender somehow turned his goal-bound effort over the bar from just a few yards out.
It mattered not though, as just minutes later Rovers were celebrating the opener. A handball decision went against an Exeter player in the box and that gave Molyneux the chance to open his account for the season. The man who posted 31 goal contributions last term got off the mark here as he duly despatched the spot-kick past Joe Whitworth to send the home fans wild.
Here's how we rated the Rovers players on matchday one:
17. Sean Grehan N/A
On at the death in place of goalscorer Molyneux. Photo: Andrew Roe/AHPIX LTD