Following an early injury to goalkeeper Hugo Lloris, striker Harry Kane scored twice in the opening 13 minutes to put us firmly in control.
However, Jamie Vardy pulled one back for the visitors on 38 minutes, with Wes Morgan making us rue earlier missed chances when he made it 2-2 five minutes after the break.
Kane completed his hat-trick from the penalty spot after David Nugent fouled Danny Rose to put us back in front on 64 minutes, before Christian Eriksen's shot was saved but cannoned back into the net off Jeff Schlupp to make it 4-2 with five minutes remaining.
Nugent managed a 90th minute reply for the Foxes, but we had done enough.
Spurs (4-3-2-1): Lloris (Vorm 4), Walker, Vertonghen, Dier, Rose, Mason (Dembele 88), Bentaleb, Townsend (Paulinho 58), Eriksen, Chadli, Kane. Substitutes (not used): Davies, Chiriches, Lamela, Adebayor.
Leicester (5-4-1): Schmeichel, De Laet, Morgan, Upson (Wasilewski 46), Huth (Mahrez 76), Schlupp, Nugent, James, Cambiasso (King 86), Vardy, Ulloa. Substitutes (not used): Schwarzer, Konchesky, Drinkwater, Kramaric.
Goals: Spurs – Kane 6, 13, 64 penalty, Schlupp og 85; Leicester – Vardy 38, Morgan 50, Nugent 90.
Yellow cards: Spurs – Chadli, Rose; Leicester – Nugent.
Referee: Mike Dean.