Rovers were one of the pre-season promotion favourites, but have spent the early part of the campaign languishing in the bottom half of the table.
But they showed their quality in this match with some slick passing and the only criticism was that they should have had more goals to show for their dominance.
Rovers started in a lively fashion and set the pattern when Brian Stock had an angled volley well saved by Shane Higgs in the fifth minute.
Adam Lockwood sent a header flashing across the face of goal following a tenth minute corner, before Mark Wilson had a left-foot effort saved four minutes later as Rovers kept up the pressure.
The Cheltenham defence finally cracked in the 18th minute when Lewis Guy raced onto a superb pass from James Hayter to flick the ball past the advancing Higgs and into the net.
Although they were being out-played, Cheltenham never gave up the fight and looked particularly dangerous at set pieces.
Michael Townsend had a terrific header well saved by Neil Sullivan following a 39th minute free-kick and Ashley Vincent fired wide when he should have done better early in the second half.
But the visitors were left with a mountain to climb when Matthew Mills added the second with a diving header following a corner from Stock in the 58th minute.
Rovers had numerous chances to add to their score but Paul Heffernan was unlucky to see a shot cleared off the line and went close on two more occasions following goalmouth scrambles.
Town battled to the finish with hard-working striker Damian Spencer missing a good chance, before substitute Paul Connor had an overhead kick tipped onto the bar by Sullivan six minutes from time.