The Gunners took the lead in the North London derby against the run of play when Mesut Ozil scored on 11 minutes.
But we continued to apply pressure and we finally made a breakthrough on 56 minutes, Kane scoring at the back post after Erik Lamela's corner was flicked on into his path.
Kane then produced a magnificent header from Nabil Bentaleb's cross on 86 minutes to win the match and take his tally to 22 for the season.
Spurs: Lloris, Walker, Vertonghen, Dier, Rose, Mason (Paulinho 90+4), Bentaleb, Lamela (Stambouli 89), Dembele (Chadli 75), Eriksen, Kane. Substitutes (not used): Vorm, Davies, Fazio, Soldado.
Arsenal: Ospina, Bellerin, Mertesacker, Koscielny, Monreal, Coquelin (Akpom 89), Cazorla (Rosicky 68), Welbeck (Walcott 78), Ramsey, Ozil, Giroud. Substitutes (not used): Szczesny, Gibbs, Gabriel, Flamini.
Goals: Spurs – Kane 56, 86; Arsenal – Ozil 11.
Yellow cards: Spurs – Kane, Mason; Arsenal – Monreal, Welbeck, Koscielny, Giroud, Ramsey.
Referee: Martin Atkinson.