Troy Brown was the Cheltenham hero when he scored from close range after the home side failed to deal with Matt Richards's dangerous right-wing free-kick.
The home side, who were second best all afternoon, missed their best chance of the game moments earlier when Stewart Drummond headed wide of the target from three yards when he looked certain to score.
Cheltenham had the better of the first half and produced the better chances. They were denied twice in quick succession midway through the half by home goalkeeper Barry Roche who made two superb saves.
In the 23rd minute he spread himself well to smother Jermaine McGlashan's close-range effort before tipping over a header from Byron Harrison at full stretch a minute later.
The Robins continued to press and went close again on the stroke of half time but were foiled by a string of goal-line clearances as Harrison saw two efforts blocked before Brown volleyed the final rebound wide.
Morecambe's best effort came from midfielder Andy Fleming as his shot from the edge of the area forced an excellent save from Scott Brown.