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."
Torquay United 01 Olejnik 03 Nicholson 04 Ellis Booked 05 Robertson 18 Oastler 07 Mansell 10 O'Kane 11 Morris 19 Stevens (Rowe-Turner - 79' ) 22 Lathrope Booked 23 Atieno (McPhee - 80' ) Substitutes 13 Rice 02 Rowe-Turner 20 Aldred 16 McPhee 24 Yeoman Swindon Town 35 Foderingham 04 Flint 07 Caddis 36 Ridehalgh 08 Ferry 10 Ritchie 12 McCormack 24 Smith 23 De Vita (Gabilondo - 67' ) 29 Magera (Murray - 46' ) 33 Jervis (Connell - 80' ) Substitutes 27 Cibocchi 13 Risser 21 Gabilondo 17 Connell 34 Murray