The Cumbrians had seemed destined to head the table after Michael Bridges shot them into a 40th minute lead.
The ex-Leeds and Sunderland striker's goal would have been a fitting way for Carlisle to take first place.
Midfielder Chris Billy started the move deep in his own half with an impudent chip over a bemused Robins player.
Derek Holmes joined the fun with a clever pass down the flank to Karl Hawley. Hawley's slide-rule cross made it easy for Bridges, who couldn't miss from inside the six-yard box.
Carlisle's front three who exuded confidence and menace all afternoon threatened to put the game beyond Town.
Holmes had a goal bound shot blocked bravely by Dave Bird and Hawley combined well with Bridges before shooting wide.
All three were involved in a scintillating move that ended with Cheltenham keeper Shane Higgs brilliantly saving Adam Murray's close-range effort.
But despite Carlisle's exuberance, Town refused to buckle. Kayode Odejayi had an early header tipped over the bar and Bird flapped at a great chance from only 12 yards.
He came closer in the 22nd minute. His shot seemed destined to go in until Carlisle keeper Keiren Westwood and defender Paul Arnison conspired to squeeze the ball on to the left post.
Cheltenham were forced to gamble in the latter stages and threw men forward, but it was not until the allotted three minutes of injury time had passed that they got their reward.
Referee Mathieson evoked the fury of the Carlisle bench by awarding the visitors a free-kick just inside home territory.
From the resulting move, JJ Melligan was able to cross into the Carlisle area and Bird headed into the six-yard area, where Gray's panicking attempted clearance flew into his own net.