Marcus Stewart's second-half header was enough to give Yeovil victory at Huish Park as Swansea's new manager Roberto Martinez watched from the stands. Stewart rose to head in Nathan Jones' free-kick in the 55th minute.
Swansea came closest to finding an equaliser in the final stages when Andy Robinson's shot was cleared off the line by Jones.
Stewart nearly made the game safe seconds later but he narrowly failed to connect with Arron Davies' low cross.
Yeovil: Mildenhall, Forbes, Skiverton, Guyett (Rose 79), Jones,
Brittain (Davies 76), Cohen, Kalala, Sweeney (Morris 76), Gray,
Stewart.
Subs Not Used: Barry, Law.
Booked: Jones, Morris.
Goals: Stewart 56.
Swansea: Oakes, Amankwaah, Austin (Craney 20), Lawrence,
Painter, Britton, Tate, O'Leary, Robinson, Trundle,
Abbott (Jones 76).
Subs Not Used: Gueret, Graves, Butler.
Booked: Amankwaah, Abbott, Tate.
Att: 5,984
Ref: T Bates (Staffordshire).