Christian Eriksen hit the bar with an early free-kick, but it was following a set piece at the other end that Chelsea took the lead a minute before the break.
Willian's free-kick was knocked down in the area, with John Terry firing into the net from 12 yards out.
The Blues added a second goal on 56 minutes, Diego Costa's angled shot from the left taking a deflection off Kyle Walker and flying inside the near post.
We kept plugging away in search of a route back into the contest, but Chelsea held firm to claim the trophy.
Spurs: Lloris, Walker, Vertonghen, Dier, Rose, Mason (Lamela 71), Bentaleb, Townsend (Dembele 61), Eriksen, Chadli (Soldado 80), Kane. Substitutes (not used): Vorm, Davies, Fazio, Stambouli.
Chelsea: Cech, Ivanovic, Terry, Cahill, Azpilicueta, Fabregas (Oscar 88), Zouma, Ramires, Hazard, Costa (Drogba 90+3), Willian (Cuadrado 76). Substitutes (not used): Courtois, Luis, Ake, Remy.
Goals: Chelsea – Terry 45, Walker own goal 56.
Yellow cards: Spurs – Dier, Bentaleb; Chelsea – Willian, Cahill, Cuadrado.
Referee: Anthony Taylor.