Meanwhile, Kane's haul moved him two ahead of Romelu Lukaku in the race for the Premier League's golden boot award with 26 goals ahead of Sunday's season-finale against Hull City.
Son Heung-min also scored twice as Spurs continued to shrug off any disappointment following Chelsea's title win.
Son's double means that he has become the third Spurs player to reach the 20-goal mark this season with Kane and Dele Alli.
Tottenham boss Mauricio Pochettino says Harry Kane is "one of the best strikers in the world", and insists the club can keep their best players this summer. We have Hull away and I am looking to get a couple of goals hopefully.
"Going into the Leicester game two behind, I was hoping to get one or two and keep myself in the race for Sunday so to get four and win 6-1 - I couldn't have dreamed of it".
England global Kane, who hopes to add to his tally at relegated Hull on Sunday, said: "I've been thinking a lot about getting on the scoresheet this week". The England global scored four goals away to Leicester last night to move top of the pile heading into the final weekend of the season.
"It is very clear we will keep the players we want to keep and we will maybe sell the players we want to sell", said Pochettino.
"We have our (transfer) targets and we will see if we can achieve them", Pochettino said.
"It's a big decision I think for Daniel Levy and the club".
Tottenham moved to 83 points on the season, two more than Leicester's title-winning total a year ago. If you get beaten 6-1 there are no positives.
It wasn't a costly miss though as Kane gave the visitors the lead soon after when a wonderful long ball from Toby Alderweireld found Son, who ran towards goal before playing the ball to Kane, who in turn flicked the ball into the net.
The Tottenham striker has 26 league goals to his name, two more than Lukaku (24) and three more than Sanchez (23).
The South Korean scored the other two goals with Ben Chilwell getting Leicester's consolation. That's the one position, but I don't know who it is. Leicester basically allowed Spurs to have shooting practice towards the end of the game, and Kane didn't need further invitation, coolly finishing from just outside the box with a strike that left Foxes keeper Kasper Schmeichel wrong-footed. They have a tough game against Arsenal but there's still one more game.
But former Premier League manager Curbishley believes that the England global is "fooling" goalkeepers with the speed of his shooting, whilst delivering a glowing verdict of his talents.