Kane's four goals propelled him to the top of the Golden Boot race, ahead of Everton's Romelu Lukaku and Arsenal ace Alexis Sanchez.
South Korea's Son Heung-Min scored twice for Tottenham, who swept to their 11th win in their last 12 league games after Leicester's Ben Chilwell briefly reduced the deficit in the second half.
Sissoko was given a rare start by his manager Mauricio Pochettino, the sixth Premier League match he has started this term. "But it's true that Harry Kane is our main striker and one of the best in the world", he said.
We had one marvellous year in my time there - 1986-87 when we reached the FA Cup final and finished third - that people still ask me about when I go back to the Lane.
"It's a special bond and I don't think you always get that at clubs, that's why we've got to hold onto that, make that motivate us to hopefully be out there next year at Wembley lifting a Premier League together". There are no positives. It ended; Leicester 1 - 6 Tottenham.
"But we're going into bigger and better things, and the new stadium is going to be unbelievable".
Son's strike put Spurs in total control but it was the build-up which caught the eye as Leicester were completely pulled apart.More news: Microsoft Surface Pro 4 refresh images leaked, may launch on May 23
Alli was the catalyst, taking possession on the edge of the area and impudently bypassing the Leicester defence with a sublime chipped pass to Son, whose half-volley lacked power but still had enough accuracy to beat Schmeichel.
- 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).
Kane. He is now in pole position to claim the golden boot after his four-goal haul which took him past last season's total.
The 2016/2017 English Premier league winners Chelsea will be crowned champions on Sunday, May 21 when they host the already relegated Sunderland at the Stamford Bridge.
Son, Alli and Kane were relentless, epitomising Spurs' quality and work rate.
Shakespeare switched his side to a back three for the second half and the change triggered a response, with Mahrez testing Lloris from 20 yards and Marc Albrighton seeing a promising opening snuffed out by a fine Eric Dier block.