We took the lead 19 minutes into the Fourth Round tie when Andros Townsend converted his second penalty inside a week after Roberto Soldado was brought down in the area by Liam Moore.
The Foxes hit back on 83 minutes through Leonardo Ulloa before Jeff Schlupp found the net in stoppage time to send the visitors through into Round Five.
Spurs (4-2-3-1): Vorm, Chiriches, Kaboul, Fazio, Rose, Dembele (Kane 87), Capoue, Lamela, Paulinho, Townsend (Eriksen 64), Soldado (Adebayor 71). Substitutes (not used): Friedel, Dier, Davies, Stambouli.
Leicester (4-2-3-1): Schwarzer, Simspson, Morgan, Moore (Wasilewski 26), De Laet, King, Drinkwater, Vardy (Nugent 72), Kramaric (Albrighton 72), Schlupp, Ulloa. Substitutes (not used): Hamer, Konchesky, Cambiasso, Knockaert.
Goals: Spurs - Townsend (pen) 19; Leicester – Ulloa 83, Schlupp 90+2.
Yellows: Leicester – Moore, Kramaric, Wasilewski, Ulloa.
Referee: Robert Madley.