Carlisle had the first major chance when the ball fell to Derek Holmes and he turned and shot, but Alan Julian in the Stevenage goal saved comfortably.
Carlisle then took the lead in the 23rd minute after Tom Cowan's cross was headed into the bottom corner by Peter Murphy.
Stevenage pressed forward looking for the equalising goal with Jon Brady finding Darryn Stamp at the back post with a good cross, whose header was deflected over.
Elding blazed over from just inside the area, George Boyd hit a well worked free kick over the crossbar while Michael Warner had a good run into the area, cutting inside onto his left foot before seeing his goalbound shot saved by the feet of Matt Glennon.
In stoppage time there was a late flurry with the ball bouncing around in the Carlisle penalty area with shots raining in from all angles.