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:
13. Harry Clifton 5
Pressed with intent but nothing tangible at the end of it. Photo: Howard Roe/ahpix.com
14. Rob Street 7
Came on, possibly with a point to prove against his old club. Had a shot for a penalty turned away but got over it by adding gloss with his stoppage time lob. Photo: Bruce Rollinson
15. Joe Sbarra 5
Booked cheaply late on but redeemed himself when he played a key role in Street's goal. Photo: Howard Roe/AHPIX LTD
16. Joe Ironside 5
With his first touch he could have scored but somehow scuffed it wide from a few yards out. Photo: Howard Roe/ahpix.com