Son's 20th goal of the season was just reward for Tottenham's dominance, but Leicester got one back in 59th minute.
Mauricio Pochettino has stressed the importance of Spurs finishing the season well, despite Chelsea claiming the title.
It was just Kane's 29th appearance of the campaign, seven fewer than Lukaku, eight fewer than Alexis Sanchez and five fewer than Diego Costa.
Everton's Romelu Lukaku is second on 24 goals but Kane is well on course to nail down the goalscoring prize heading into Tottenham's final fixture at Hull on Sunday.
- Harry Kane is the fifth player in Premier League history to score 25-plus goals in successive seasons (Robbie Fowler, Thierry Henry, Alan Shearer and Robin van Persie are the others).
Riyad Mahrez and Jamie Vardy almost conjured up a move reminiscent of last season's title-winning campaign, with Vardy peeling off his man, only to fire his shot straight into the arms of Hugo Lloris.
Leicester was on the back foot instantly when Son shot over before Jamie Vardy fired straight at Lloris.
29th min: It had been an open game up for the first half an hour, but Kane made sure to grab the game's first goal and put his side in command.
Leicester defender Christian Fuchs was caught out by Toby Alderweireld's deep ball which allowed Son to burst into the area.
It was nearly two with their next attack as Alli saw his header from a Ben Davies cross well-saved by Kasper Schmeichel.
Tottenham's Victor Wanyama, left, and Leicester's Wilfred Ndidi battle for the ball during the English Premier League soccer match between Leicester City and Tottenham Hotspur at the King Power Stadium in Leicester, England, Thursday, May 18, 2017. Spurs' keeper, Lloris, had rushed out of his box to clear the ball.
With Leicester's minds turning to their post-season holidays, Kane had acres of space to pilage the hosts' defence and he completed his hat-trick with a superb 20-yard strike in the 89th minute. 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. They absolutely dismantled the defending champions on their home patch, winning 6-1. "He is great, one of the best strikers in the world and now we try to keep going and he tries to finish in the best way and then we look forward to next season".