A 51st minute header from Richie Foran gave Carlisle a win that could prove crucial in retaining their Football League status.
Foran rose between two defenders to nod home a right wing cross from Darren Kelly and condemn fellow strugglers Rovers to a morale-sapping defeat.
The home side was booed off, having failed to equalise against a team reduced to ten men by Jon McCarthy's 69th minute sending off for a second caution.
McCarthy was dismissed for a late challenge on Rover's substitute Simon Bryant, just five minutes after collecting his first booking for encroaching at a free kick.
Rovers had taken a 33rd minute lead when Brian Shelley's poor clearance set up Giuliano Grazioli, who fired home his 11th goal of the season from ten yards.
The result might have been different if Rovers had held their lead until half time. But seconds before the break poor defending allowed Shelley to make amends for his earlier error.
The full back looked to of been crowded out when surrounded by three defenders inside the Rovers box, but still managed to get a pass in to striker Craig Farrell, who lashed home a low drive from 15 yards.
With Carlisle keeper Matt Glennon in impressive form, there was no way back for Rovers. The home side huffed and puffed without getting many attempts on goal.
When Glennon saved bravely at the feet of sub David Gilroy in injury time, Carlisle's victory was assured and they were able to make the long trip home boosted by three priceless points.
For Rovers the future looked bleak. Disgruntled supporters made their feelings known at the final whistle when chants of "what a load of rubbish" echoed around the Memorial Stadium.