Christian Eriksen finished off a sweeping move on 81 minutes to round off a comfortable win. They move onto 44 points, level with fourth-placed Liverpool, who take on Manchester City at Anfield tomorrow.
Kane has now scored 20 league goals this season, three more than the next most prolific, Liverpool's Mohamed Salah.
Eriksen played the killer a pass, an absolutely brilliant ball out wide to Serge Aurier and he took one touch before delivered what appeared to be a shot.
Chelsea were unable to pierce Leicester's defence and were second-best for long periods at Stamford Bridge, even after visiting left-back Ben Chilwell was sent off for a second bookable offence midway through the second half.
With 22 minutes on the clock, the visitors thought they had taken the lead when new striker Cenk Tosun headed on a corner and Wayne Rooney pounced, only for him to be flagged for offside.
Kane worked hard, dropping deep to bring centre-backs Phil Jagielka and Mason Holgate out of position and that created space for Pochettino's players to run into.
It was Kane's 98th goal for Spurs in the Premier League making him the club's all time top scorer in the competition.
Rooney's late booking for an ugly chop on Jan Vertonghen encapsulated Everton's frustration and Tottenham polished off a handsome win with a stunning fourth goal, Dele Alli's back-heel teeing up Eriksen to hammer emphatically past Pickford.
He spun on a dime in the 47th minute to leave his mark in the dust and smartly, if not inadvertently, whipped the ball into Kane's path, who was left with the easiest of tap ins.
"He loves Tottenham and only that everyone wants to win - us, the club, (chairman) Daniel Levy, the players, the fans - everyone wants to win, and wants to win in the place you love".
Son was involved again as Alli had a chance to make it three with 53 minutes played but could only steer his attempted finish into the side netting. Then, when the second goal goes in and it's probably offside, that doesn't allow us to throw the towel in for me and not do the right things.
Let's just celebrate Kane for what he is.
Mauricio Pochettino's men will certainly look to repeat the same kind of performance they put in against Everton earlier in the season at Goodison Park.