Jon Obika's goal was enough to give Yeovil victory as the Glovers edged closer to safety in League One.
Swindon should have had a reward for their bright start but Hal Robson-Kanu had his shot well saved by Chris Weale.
The home side scored what proved to be the winner after 33 minutes when Paul Warne slipped a delicate pass to Obika, who lobbed goalkeeper Phil Smith.
Weale later saved well from Swindon's top scorer Simon Cox to ensure that Yeovil picked up all three points.
Yeovil: Weale, Hutchins, Forbes, Peltier, Smith, Warne (Murtagh 88), Roberts, Noble, Townsend, Obika, Tomlin (Rodgers 78). Subs Not Used: Jones, Welsh, Schofield.
Booked: Forbes, Weale, Noble.
Goals: Obika 33.
Swindon:
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Phil Smith, Amankwaah, Morrison (Ifil 13), Greer, Jack Smith, Robson-Kanu (Kennedy 24), Timlin, Nalis (Pook 76), McNamee, Paynter, Cox. Subs Not Used: Brezovan, Razak.
Booked: Jack Smith, Amankwaah.
Att: 5,476
Ref: Roger East (Wiltshire).
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