Kane scored his first goal in the 10th minute with a low drive from the edge of the penalty area. He added a second shortly afterwards from Kieran Trippier's volleyed pass.
Dele Alli claimed the third just before halftime for the Premier League runners-up and top scorers.
Midfielder Sam Clucas pulled one back but Victor Wanyama and Kane, completing his fifth hat trick of 2017 in all competitions, emphasised Tottenham's superiority with his 29th league goal of the season.
There were further goals from Ben Davies and Toby Alderweireld as Spurs followed up Thursday's 6-1 romp at Leicester with another exhilarating show.
The seventh goal enabled them to pip champions Chelsea as the league's highest scorers with 86 goals.
"We are delighted with the way we finished," Kane said.
"To win 7-1 away from home is a great end to a great season for us.
"It's massive to win the Golden Boot again. I said to retain it would be special with the injuries I've had but to score 29 goals in 30 games is something I feel proud of.
"Finishing the season with seven goals in two games is perfect, hopefully I can continue it at the start of next season."
(Reporting by Steve Tongue; Editing by Toby Davis)
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