The Cobblers were unable to muster more than a patchy performance against a side who kept their first clean sheet for eight matches after Damian Spencer had given them a 22nd minute lead.
Colin Calderwood's team are now two points outside the play-offs and must look to win their last three games, against Lincoln City, Chester City and relegation-threatened Kidderminster Harriers, to give themselves a chance of extending their season into the play-off competition.
Their hopes suffered an early setback in this game when central defender Ashley Westwood was forced off with an injury, his place being taken by youngster Luke Chambers.
That enforced change appeared to rattle the visitors and they found it difficult to achieve any fluency during an opening half of few chances that Cheltenham just about shaded.
The only goal arrived when a long ball from former Northampton player Jerry Gill was headed clear by Chambers. Cheltenham striker Steve Guinan tried his luck with a speculative shot from distance with goalkeeper Lee Harper having strayed off his line. The ball rebounded back off the post and landed for Spencer to force home the rebound from close range.
Cheltenham goalkeeper Shane Higgs had earlier made a reaction save from an Andy Kirk header and saw a shot from Sam Togwell fly past his left-hand post, although at the other end Cheltenham went close with a header from Shane Duff that was cleared off the line.
Northampton really should have squared the scores two minutes before the break but Kirk headed wide from an unmarked position after Scott McGleish had picked him out with an inviting cross.
The second half produced less flowing football than the first and as the game wore on, Northampton's attempts to claw a goal back became more and more desperate.
Kirk fired over the crossbar and Duf was forced to chase back and clear off the line after McGleish had beaten Higgs with an opportunist effort; but Cheltenham also had chances with both Brian Wilson and Martin Devaney extending Harper.
Northampton applied intense pressure in the closing stages with all but the goalkeeper and two defenders committed to attack, but Cheltenham defended resolutely and almost grabbed a second goal in the final minute when Wilson broke clear and crossed for substitute Adam Connolly, whose header cleared the crossbar.