They conceded a goal in each half, David Bird poking home in the first half and Alex Russell swinging in a superb shot from out wide in the second.
Anthony Elding came off the bench to head his first goal for Leeds with five minutes to go but it was too little too late.
Leeds were having the bulk of the early possession but Cheltenham kept their shape well and restricted the home side to a long-range effort from Johnny Howson that flew wide.
Cheltenham finally broke the deadlock just before half-time, Bird seizing on a mistake by Frazer Richardson and toe-poking it past Casper Ankergren.
The visitors almost doubled their lead a minute later when their powerful striker Damian Spencer was given a free header but glanced it wide of the post.
Leeds were booed off at half-time and no doubt got a strict talking to by Gary McAllister.
They certainly started the second half with more energy and Bradley Johnson brought the crowd to their feet after only two minutes with a dipping free-kick but Shane Higgs got across and pushed it away.
But Cheltenham went further ahead when Alex Russell curled a superb shot into the top corner from near the touchline and Elding's late goal proved nothing more than a consolation.