Running fully 50 yards, Kavanagh played the ball wide to Simon Hackney and, when his fierce shot was spilled by keeper Scott Brown, the ex-Republic of Ireland international slammed in the rebound from 12 yards. Cheltenham defended doggedly throughout, but their forays forward were few and far between and they rarely posed a problem to Carlisle's on-loan keeper, Tim Krul.
But the Robins almost went ahead when Carlisle defender Richard Keogh inadvertently sent a spectacular header hurtling towards his own crossbar from 15 yards in the 43rd minute. Earlier, Kavanagh had curled a free-kick inches over before visiting winger Lee Ridley's first-time shot was smothered by Krul.
Man-of-the-match Kavanagh then saw a 25-yard drive deflected just wide and from the resulting corner Danny Graham's header was saved before Keogh hit the same crossbar with a thunderous point-blank shot. Graham was the next villain for Carlisle, missing a simple three-yard header after good work from Cleveland Taylor before Kavanagh intervened midway through the second half.
The Cumbrians pushed on and had several chances to extend their lead with Taylor, Hackney and full-back Michael Liddle all forcing smart saves from the busy Brown. But the Robins held on and teenager Lewis Montrose jumped highest to force Krul into a full-length save with striker Paul Connor lurking.
The Robins' lack-lustre search for a late equaliser highlighted their chronic lack of firepower as their miserable away run of just one point all season continued. Carlisle meanwhile winning their second league game in a row having failed to claim all three points in their previous ten league matches.