The Robins wrested control from visitors Northampton with two goals just before half-time and made the game safe with a second-half penalty.
A headed goal from Scott McGleish four minutes into injury-time was scant consolation for the Cobblers, this result applying the brakes to their own promotion charge.
Northampton, with only one defeat away from home this season, stroked the ball around comfortably in the opening 20 minutes and called Robins goalkeeper Shane Higgs into action on a series of occasions.
Higgs touched a cross-cum-shot from Pedj Bojic and a header from McGleish over the crossbar and held a snap header from Ian Taylor as the visitors threatened to take control.
Cheltenham held firm and found a way to cause problems for the Northampton defence through the vicious in-swinging corners of left-back, and former Cobblers player, Mickey Bell.
Defender Jason Crowe headed efforts from Steve Guinan and Kayode Odejayi off the line from Bell corners, while goalkeeper Lee Harper made a superb save from an Odejayi header resulting from a David Bird long throw.
The breakthrough arrived seven minutes before the break when a cross from Bell was mis-kicked by Gavin Johnson and Harper got into a tangle with Luke Chambers going for the loose ball. Guinan was on hand to score into a gaping net, his fourth of the season.
Then just moments before the break, another corner from Bell was flicked on by Mike Townsend and Odejayi pounced from close range to take his season's tally into double figures.
The second half was evenly contested with Cheltenham content to sit back on their lead, although they were given the chance to go further ahead when Odejayi, who had produced an impressive run from the halfway line, was brought down in the box by Chris Doig.
JJ Melligan sent Harper the wrong way from the spot and the contest was all but finished.
Northampton rallied in the closing stages with substitute Scott Cross hitting the post, before McGleish headed in from an Eoin Jess cross to spoil Cheltenham's clean sheet with virtually the last touch of the game.