Own goals from Danny Livesey and Zigor Aranalde wrapped up the win for Rovers, with Junior Agogo sealing the victory with the last kick of the game.
Neither team offered any indication that they could be promotion candidates and, on this showing, both will be happy to escape the drop.
It all started brightly for Carlisle, who included Newcastle winger Alan O'Brien signed on loan for a month.
Peter Murphy had already struck the post for the home side before O'Brien latched onto Derek Holmes' pass and outpaced Craig Hinton to slot home from eight yards.
With the Brunton Park fans singing for their new hero, the Cumbrians dominated for the rest of the half and Karl Hawley and Murhpy again went close.
But that was as good as it got for Carlisle as Rovers came out in the second half with fresh confidence.
Chris Carruthers should have put Rovers level when he headed inches wide when perfectly placed ten yards out.
But when the equaliser did come it was Carlisle who inadvertently scored their second of the day.
Ali Gibb, a thorn in Carlisle's side all day, crossed only for keeper Keiren Westwood to parry and Livesey was helpless as the ball bobbled off him and into the net.
With eight minutes to play it was Aranalde's turn to put the ball in his own net when he knocked Agogo's miss-hit shot into the net and wrong-footed Westwood.
With Carlisle looking bewildered and lost, they were soon conceding again, only this time they could not blame themselves.
Deep into injury time Aaron Lescott played a through ball to Agogo who lifted the ball over the onrushing Westwood from 30 yards.
At the whistle, Carlisle were booed off by their fans as Bristol celebrated a much needed win.