Terrell Forbes put through his own goal to gift Swindon the spoils and leave the Glovers without a win since the opening day of the season.
Swindon almost took the lead in the 35th minute, only to be foiled by a goal-line clearance by Craig Alcock.
Six minutes later they were ahead when Forbes headed into his own net from close in after Billy Paynter nodded on a Jon-Paul McGovern cross.
Yeovil showed plenty of endeavour but created few chances of note.
Yeovil Town player-manager Terry Skiverton told BBC Somerset:
"Once they got the goal on 40 minutes they were very hard to break down in the second half.
"I felt that luck was against us. We lost Gavin Tomlin to a late fitness test and Sam Williams came off after 10 minutes and then my captain Craig Alcock also comes off.
"I felt there were a couple of chances, maybe a penalty and I think there was a handball in there as well."
Swindon manager Danny Wilson told BBC Wiltshire:
"We looked reasonably solid, I thought we passed the ball very well.
"I think the score could have been more emphatic with the chances we had, and I don't think David [Lucas] had a serious save to make.
"Defensively we've done very well throughout the team, we've worked very hard, particularly in the second half."
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