A Ryan Shawcross own-goal broke the deadlock and Son Heung-min got in on the act with a fine second before Kane's double moved him on to 50 goals for club and country in 2017.
It marked an emphatic return to winning ways for Spurs, who had only taken two points from their past four Premier League matches.
"That was what we needed, we had to get the first goal and we did that and that was it. We were on fire from there," Kane told BBC Sport .
"Coming off a few bad results we were always going to be up for it.
"Son was very good. He [created] the first goal and it was a great finish for the second, that set us on our way and got everyone firing.
"We look forward to the busy period now."
Manager Mauricio Pochettino also singled out Son for praise alongside his top scorer.
"Sonny was great, amazing performance, I think he was one of the key players," he said. "But the team performance was fantastic."
"[Kane] had chance to score more, because in the first half he was clear and had a great chance but I am very happy with him."