Nacer Chadli fired us ahead on six minutes after getting on the end of Danny Rose's cross, but the visitors levelled on 20 minutes through Ki Sung-Yeung.
Ryan Mason's first Premier League goal saw us restore our lead six minutes after the break, with Andros Townsend making it 3-1 on the hour mark.
An 88th-minute strike from ex-Spur Gylfi Sigurdsson set up a tense finish, but we held on to claim the points.
Spurs (4-2-3-1): Lloris, Walker, Vertonghen, Dier, Rose (Davies 78), Mason, Bentaleb, Townsend (Dembele 65), Eriksen, Chadli, Kane (Soldado 76). Substitutes (not used): Vorm, Chiriches, Paulinho, Lamela.
Swansea (4-3-3): Fabianski, Naughton, Williams, Fernandez, Taylor, Cork, Shelvey (Montero 73), Ki, Routledge, Gomis (Oliveira 12), Sigurdsson. Substitutes (not used): Tremmel, Amat, Britton, Emnes, Rangel.
Goals: Spurs – Chadli 7, Mason 51, Townsend 60; Swansea – Ki 20, Sigurdsson 88.
Yellow cards: Spurs – Dier.
Referee: Michael Oliver.