Leeds looked the classier outfit and could have had the game wrapped up, but Town kept going and secured only their second home win and second clean sheet of the season.
The goal arrived with only four minutes left to play when Leeds goalkeeper Dave Lucas threw a ball out to defender Frazer Richardson but Cheltenham's Dean Sinclair got there first.
Sinclair played it to Andy Lindegaard and although his defence-splitting ball was headed clear by Lucas, Steven Gillespie had the presence of mind to divert it back into the net from the edge of the area.
Cheltenham had earlier rode their luck a little bit with Jermaine Beckford in particular having an off-day with his shooting.
Beckford sent an early shot over the crossbar and was then denied by a fine last-ditch tackle from David Bird right in front of goal.
Beckford hit the crossbar with a shot just before half-time and sent a lob shot inches wide but his most glaring miss came midway through the second half when David Prutton won a header against Cheltenham's diminutive left-back Alan Wright.
The ball travelled across to the far post with goalkeeper Shane Higgs struggling to make up ground although Beckford, with the goal gaping before him, blasted his shot wide from six yards.
Beckford knew his luck was out 15 minutes from time when a free-kick from Jonathan Douglas was spilled by Higgs and although Beckford was first on the scene to head into the empty net, the assistant referee had already raised his flag for offside.
Gillespie's goal visibly shook the Leeds players and the former Liverpool trainee almost added another in the final minute, when he ran on to a through ball but curled his shot just wide.