Emmanuel Adebayor was at the double - a Chico Flores own goal sandwiched in between his efforts - as we raced into a three-goal lead.
Wilfried Bony replied for the Swans in the closing stages, but there was to be no comeback.
Swansea: Tremmel; Rangel, Flores, Williams, Davies; Routledge, Amat, Britton, Pozuelo, Shelvey (Lamah, 51); Bony. Unused subs: Cornell, Taylor, Tiendalli, Vazquez, Richards, Donnelly.
Spurs: Lloris; Walker, Chiriches, Dawson, Rose; Lennon (Naughton, 79), Bentaleb, Dembele, Eriksen, Chadli (Sigurdsson, 71); Adebayor. Unused subs: Friedel, Capoue, Holtby, Defoe, Soldado.
Goals: Swansea - Bony (78). Spurs - Adebayor (35, 71), Flores own goal (53).
Yellow cards: Swansea - Amat, Bony. Spurs - Rose.
Referee: Mr M Atkinson.