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:
5. Jack Senior 6
Did well against dangerous Thomas down his flank first half and posted highest number of tackles. Played the role of panto villain after Dieng's foul on him earned the Cheltenham man an early bath. Photo: Howard Roe/AHPIX LTD
6. Owen Bailey 6
Solid enough in the engine room before switching to centre-half in a late tactical change. Photo: Howard Roe/AHPIX LTD
7. George Broadbent 6
Some nice pick-outs and plenty of hunger to get stuck in but couldn't produce any killer passes that pierced the Cheltenham defence. Photo: Craig Hawkhead/AHPIX LTD
8. Patrick Kelly 6
Recalled for a first start in two months. Plenty of drive early doors and some neat touches. Replaced by Clifton for the last half-hour. Photo: Bruce Rollinson