Barry Corr hit the only goal as Swindon weathered a first-half storm to avenge the home defeat to Yeovil in September. Robins goalkeeper Peter Brezovan was the busier of the two in the first period and James Walker saw a superb 25-yard shot hit the post.
But the visitors had more of the play after the break and scored when Yeovil lost possession and Corr slid home a low shot from 10 yards.
The home side then had Terry Skiverton sent off for a foul on Corr late on.
Yeovil: Mildenhall, Peltier, Skiverton, Forbes, Nathan Jones (Rose 80), Warne (Owusu 67), Dempsey (Barry 76), Way, Stieber, Stewart, Walker.
Subs Not Used: Cochrane, Bircham.
Sent Off: Skiverton (78).
Swindon: Brezovan, Comminges, Aljofree (Nicholas 24), Ifil, Vincent, McGovern, Peacock, Easton, Mohamed (Allen 86), Corr (Paynter 82), Cox.
Subs Not Used: Pook, Sturrock.
Booked: Corr.
Goals: Corr 66.
Att: 6,539.
Ref: Danny McDermid (Middlesex).
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Interview: Yeovil manager Russell Slade
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