In so doing the Robins leapfrogged above their rivals in the League One relegation battle, consigning Brentford to their fourth consecutive League defeat and now their 11th match without a win.
Cheltenham appeared to be a side transformed from that which has struggled so badly in recent matches, while Brentford are desperately low on confidence and in need of some inspiration.
The home side made the perfect start to a lively first half when they scored after only five minutes.
The goal resulted from a long throw taken by David Bird that found its way to striker Kayode Odejayi. The Nigeria-born frontman deflected a subtle header just inside the far post with goalkeeper Clark Masters scrambling to make up ground.
Masters touched a pile-driver from Damian Spencer over the bar shortly afterwards and then fell upon an angled drive from Odejayi as Cheltenham enjoyed plenty of success with high balls aimed into the box for their big frontmen.
Brentford were able to play only in patches but they too created some presentable chances.
A mis-hit clearance from Cheltenham goalkeeper Shane Higgs fell to midfielder Thomas Pinault. Higgs dived full-length to push aside his first-time shot and then made a top-class save from a Clyde Wijnhard header to keep his team's lead intact.
At the other end, Masters dived bravely to block a Gavin Caines effort at the end of a half that should have supplied more goals for the noisy Friday night crowd.
Cheltenham continued to dictate the play after the break and could have extended their lead with headed chances for both Spencer and John Melligan, the quality of the crossing coming from both sides of the pitch proving difficult for the Brentford defence to deal with.
Any remaining nerves among the home fans were dispelled 15 minutes from time when Odejayi took a long ball from Jerry Gill on his chest before thumping a shot beyond Masters. It was a classy goal to finish off a performance the home fans have waited a long time for.