Grant McCann's side looked as if they were destined to not break the deadlock against opponents that were proving stubborn despite playing most of the second half a man light.
But Jamie Sterry and sub Rob Street notched late on to spark joy in the away end.
The first half was a tight, tense tussle with neither side creating a plethora of chances. The closest Rovers came was a snapshot from Jordan Gibson that was straight at Joe Day, whilst Jordan Thomas fired a fierce effort just wide of Ted Sharman-Lowe's left-hand post in response.
Early in the second half came the turning point when Cheltenham's Tim Dieng was shown a second yellow card for a lunge on Jack Senior. With a man advantage, Rovers looked to turn the screw and Gibson struck the crossbar from range almost immediately.
But Cheltenham were a tough nut to crack. Just as it looked as though spoils would be shared, up popped Sterry with a vicious effort for his first Rovers goal. Street then added gloss with a classy lobbed finish in stoppage time.
Here's our player ratings from Cheltenham:
1. Ted Sharman-Lowe 6
Was alert first half to act as a sweeper-keeper and largely untroubled all afternoon in truth. Photo: Howard Roe/ahpix.com
2. Jamie Sterry 8
Another slick display with some good touches going forward. Tried to make inroads as best he could and then capped off his day with a belting winner for his first goal in a Rovers shirt. Photo: Howard Roe/AHPIX LTD
3. Tom Anderson 6
Too often his hopeful punt didn't find its intended target. Defensively he took care of his duties tidily enough Photo: Bruce Rollinson/AHPIX LTD
4. Richard Wood 5
A few iffy moments when Miller and Dieng escaped his watch. As blatant a yellow as you'll ever see right on half-time when he clattered Thomas to halt a breakaway. Photo: Bruce Rollinson