Leeds were again unchanged, while Cheltenham gave a debut to defender Richard Keogh, who completed his loan move from Bristol City in time.
Jermaine Beckford almost added to his 17 goals for the season inside the first minute when his 25-yard shot was heading for the bottom left corner until Cheltenham keeper Shane Higgs hurled himself into a one-handed save.
Damian Spencer wasted a good chance for the visitors by spooning his shot high into the crowd and Leeds striker Tresor Kandol missed an even better opportunity by heading over the bar from inside the six-yard box when Bradley Johnson picked him out with a perfect cross from the left.
Keogh marked his debut by collecting a yellow card for bringing down David Prutton in full-flight, but it wasn't long before Cheltenham were celebrating a gifted goal.
With 38 minutes gone, Leeds defender Frazer Richardson lost control of the ball just outside his penalty box and David Bird pounced to smash the ball past Danish keeper Casper Ankergren.
It was Bird's fourth goal of the season and reminded Leeds that their lowly opponents were fighting for their lives.
Leeds continued to lack sharpness near goal with Beckford and Lubo Michalik missing the target in rapid succession just before the break.
Johnson had a fierce free-kick well saved by Higgs soon after the break, but Beckford was just too high with another shot on the turn as Leeds left their fans frustrated.
Dougie Freedman replaced Jonny Howson for Leeds in the 62nd minute, but two minutes later Alex Russell's speculative shot from left of the penalty box flew past Ankergren into the far corner for Town's second.
Anthony Elding and Andrew Hughes also left the bench and Elding headed home Neil Kilkenny's cross in the 85th minute, but Cheltenham held on for the points.