Shaun Harrad was on-target for the third game in succession as Cheltenham's unbeaten start to the season continues.
The game was played in difficult weather conditions, and the players were taken off the pitch midway through the first-half after a thunder storm.
The only goal of the game was scored in the 72nd minute - Billy Jones' corner was headed in by Harrad.
Yeovil Town won for a club record 8th time in a row. Bristol Rovers also won, Cheltenham drew and Bristol City lost in the Severnside derby.
There were wins today for both Bristol clubs and Yeovil Town. Swindon Town could only draw and Cheltenham Town slipped to defeat.
Bath have beaten West Country rivals Gloucester 32 - 5 in the LV= Cup.