Kane netted a brace, won a penalty that was successfully converted by Andros Townsend and laid on the hosts' final goal at White Hart Lane, scored by Nacer Chadli.
The 21-year-old now has six goals in his past six outings and 16 across all competitions this season - bettered only by Manchester City's Sergio Aguero among Premier League frontmen.
He would have a strong case for a place in Roy Hodgson's international squad if such form continues until the next round of international matches in March, although Kane is unconcerned by the growing clamour for him to be rewarded with a debut at the highest level
"I'm just enjoying it," he told BT Sport. "I just want to be playing. We've had a lot of games over Christmas and it’s been great for me.
"Hopefully I can keep it up and keep doing the best I can for the team. The most important thing is that we're winning and pushing up that table."
On a stirring Tottenham display that came after Diego Costa opened the scoring for Chelsea, Kane added: "It shows how good a team we are. To score five goals, and that's one of the best defences in the world, shows that we're really coming together.
"I'm delighted with that win. We've kept yup our run and hopefully we can take that into the games ahead."
Tottenham coach Mauricio Pochettino is confident Kane's form can take him beyond the 20-goal mark this season but was also keen to focus on a superb team effort.
"Yes, why not," he told BBC Sport. "He works hard every day and after he's had the opportunity to play he has shown his skills.
"But we need to recognise the team because the team performance was great today and we need to keep this feeling for the next step."
