In addition, Kane's four-goal night meant he became the fifth player to score three or more Premier League hat-tricks in a single season.
Kane scored again in the 88th minute before putting icing on the cake with another fine finish two minutes into stoppage time.
Ben Chilwell pulled one back for the former PL champions nine minutes into the second half as it seemed Leicester were making a comeback, but Tottenham responded with four more goals. Harry Kane is our main striker and he is one of the best in the world.
"For us to keep our best players, a lot of clubs are interested in them, but the players we want to keep will be here next season", the Spurs boss was quoted as saying by the BBC. "Maybe we will sell the players that we want to sell".
'We are so, so calm about our key players. "They are happy here, we have an exciting project".More news: Arvind Kejriwal opposed note ban as it threatened money laundering: Kapil Mishra
Kane opened the scoring for the Lilywhites midway through the first half before Son Heung-min added a second before half-time.
It was 4-1 soon after when Kane gave the ball to Son a long out from goal but he struck a wonderful curling shot into the back of the net past the helpless Schmeichel.
Chelsea has taken the trophy off Leicester, which astonishingly won the title last season but collapsed this year and is now 11th.
This was visitors 13th win in their last 16 games in all competitions, having already cemented second place in the league standings with 83 points.
He is two ahead of Everton striker Romelu Lukaku going into the final day of the Premier League season.More news: South Korea, Japan Countries seek to lower tensions over 'comfort women'
Tottenham challenged Leicester for the title last season, before eventually finishing third.
Leicester City's Jamie Vardy (left) and Tottenham Hotspur's Mousa Dembele vie for the ball. With Fuchs trailing behind, Son teed up Kane to sweep in from six yards.
It was nearly two with their next attack as Alli saw his header from a Ben Davies cross well-saved by Kasper Schmeichel.
Any hopes of a Foxes fightback were extinguished soon after as Kane restored their two-goal advantage from a delicious cross from Toby Alderweireld.
Kane headed in from point-blank range after more neat work from Son and the South Korean grabbed his own double in the 71st. The 23-year-old blasted a low shot from the edge of the area that seemed to fool Schmeichel as it flew beneath him and into the net, before being granted time and space to produce an nearly identical finish to cap a dominant display.More news: Minister McHugh is backing Varadkar for leadership
And Kane had not finished when he scored again in stoppage time, with nearly a carbon copy of his third, beating Schmeichel low to his right from the edge of the area.
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