Ronan Murray grabbed the winner as Torquay continued their fine form at the expense of Cheltenham.
The hosts took a first-half lead when Craig Stanley's corner was powerfully headed home by Guy Branston - his second goal in two games.
After concerted pressure from the Gulls, Murray sealed the win with a clinical finish from close range.
The Robins notched a late consolation through Danny Andrew's thumping free-kick but the hosts held out.
Torquay United manager Paul Buckle told BBC Radio Devon:
"We're always delighted with the result when you win, but we've done it in style tonight.
"In my opinion Cheltenham didn't deserve to be anywhere near the game - I thought we bossed it all night and we were dominant.
"We thoroughly deserved the win, it would have been a travesty if we'd only got a point, so we got what we deserved and we could have scored a lot more."
Cheltenham manager Mark Yates told BBC Gloucestershire:
"We were done by two poor goals, two mistakes on our part. We talked about keeping it tight, but they've got some good players and even before we make the mistake for the second goal, I felt another goal was coming anyway.
"We work on defending set pieces. I know they are good at set pieces. We made some poor decisions with the ball and some poor decisions without the ball, and we didn't do enough to get ourselves back in the game."