On-loan City player Steve Brooker scored the only goal and City defender Richard Keogh, another recent loan signing, had a strong game in the centre of the Cheltenham defence.
The win moves the Robins seven points above the relegation zone and stalled any hopes Rovers might have had of staging a late play-off challenge by winning their several games in hand.
Rovers had the best of the early exchanges and Cheltenham goalkeeper Shane Higgs had to be at his best to deny both Craig Disley and Sean Rigg with diving saves.
Rigg also found himself clean through with only Higgs to beat midway through the first half but he was thwarted by a perfectly executed last-ditch tackle from defender Shane Duff.
Cheltenham attacked only sporadically during the first half but they did have the ball in the net after 25 minutes, Damian Spencer's header from an Alan Wright free-kick being ruled out by referee Stuart Attwell for an infringement.
Higgs made further smart saves from Rigg and Rickie Lambert at the start of the second half but, with just over an hour gone, Cheltenham manager Keith Downing switched to a 4-4-2 formation and the home side finished the game strongly.
Brooker headed inches wide from Spencer's cross and the only goal arrived ten minutes from the end.
Spencer was fouled wide on the left and Wright delivered a free-kick into the area. Disley headed it clear but only as far as Craig Armstrong, who headed it back into the danger area and Brooker flicked a header beyond Steve Phillips to claim his fifth goal in the last six games.
The goal may not have been the most spectacular seen at Whaddon Road but it was greeted enthusiastically enough by the home fans, who sat through a nail-biting last ten minutes in which Rovers substitute Richard Walker blazed over the bar from a good position with his team's last chance of the contest.