Torquay striker Taiwo Atieno ended Swindon's 15-game unbeaten run with the only goal in the victory at Plainmoor.
Atieno turned in his second league goal in Torquay colours from close range after Chris Robertson headed on Eunan O'Kane's corner.
Matt Ritchie was denied by Robertson as Swindon pushed on, while Atieno missed a chance to extend the Gulls lead.
Ritchie again went close late on but his shot deflected off team-mate Alan Connell and away to safety.
VIEWS FROM THE DRESSING ROOM
Torquay manager Martin Ling told BBC Radio Devon:
"We answered all the questions today, both in the first half when we looked a good attacking unit, and in the second when we looked a good defensive unit.
"I said to the lads in the dressing room 'I think we've just matched and beat a side that will be top three this year, without doubt'.
"If you're going to beat Swindon, you need a lot of your players to perform and I think we had that today."
Swindon Town manager Paolo di Canio tells BBC Wiltshire:
"I'm very disappointed in the performance, especially in the first half. It's stupid to play in the way we did in the first half.
"Nobody helped each other, nobody was speaking.
"Today, once again, I realise that maybe my expectation is more than what we really have."