It was a match dominated by the Gulls, who had only achieved one point away from home this season going into the match, and they succeeded in putting the shackles on a Cheltenham side that had won its last two games.
Leading scorer Alan Connell scored the only goal mid-way through the second half but Torquay created numerous chances that could have given them victory by a wider margin.
Such was Torquay's domination of the first half that it was not until just before half-time that Cheltenham mustered their first shot, an off-target effort from midfielder Grant McCann.
At the other end, Torquay's Matt Hewlett and Jo Kuffour both shot wide, while defender Craig Taylor met a corner with a firm header that required David Bird to boot clear on the goal line.
Torquay's new loan signing John McAliskey was combining well with striker partner Alan Connell and a host of supporting midfield players to cause the home side all manner of problems.
Cheltenham goalkeeper Shane Higgs touched a long-range shot from James Sharp over the bar then dived to make a brilliant stop from McAliskey and palmed aside a 20-yard blast from Mamadou Sow.
Cheltenham's Brian Wilson saw a right-wing cross deflected onto the crossbar but that was the closest the home side came to scoring in the whole game. Gone was the confident passing shown in recent games as they were continually forced onto the back foot.
Torquay continued their positive approach throughout the second half and Wilson was forced to clear off the line from a Kevin Hill shot before the breakthrough finally arrived on 67 minutes.
Defender Matt Hockley's chipped pass was flicked on by Leon Constantine and Connell held off the attention of Jerry Gill before shooting past Higgs.
After taking the lead the Gulls were able to shut up shop efficiently and almost grabbed a second goal when Constantine drifted in from the left and curled a shot beyond the far post.