Ferrie Bodde and Jason Scotland were on target as Swansea broke their scoring duck at Huish Park.
It was also Swansea's first win at Yeovil in the four years since the Glovers joined the Football League.
Scotland opened the scoring on 40 minutes with a 12-yard shot from a Paul Anderson cross.
Kevin Betsy equalised for Yeovil from a free kick four minutes after the break, only for Bodde to cut in from the right and drive home 11 minutes from time.
Yeovil: Mildenhall, Lynch, Guyett, Forbes, Nathan Jones, Rose, Barry, Cochrane (Walker 79), Stewart (Warne 18), Owusu (Domoraud 84), Betsy.
Subs Not Used: Dempsey, Alcock.
Booked: Nathan Jones, Rose.
Goals: Betsy 48.
Swansea: De Vries, Rangel, Lawrence, Monk, Painter, Butler (Robinson 83), Bodde, Pratley, Anderson (Britton 82), Scotland, Feeney (Duffy 69).
Subs Not Used: Austin, Tate.
Booked: Painter, Rangel, Bodde.
Goals: Scotland 40, Bodde 79.
Ref: Peter Walton (Northamptonshire).