The South Korean worldwide charged down the left flank and in a manner similar to the first goal, he dragged his shot into the box with Kane tapping the ball into the net.
Son was the architect as he went past Kenny to surge down the left flank before eluding Mason Holgate and crossing for Kane to net from close range on 47 minutes.
Spurs, who claimed a 3-0 win at Goodison Park back in September, struggled to create much in the early stages despite enjoying the better of the play, but a chance to break the deadlock went begging as Son headed Eriksen's free-kick narrowly over.
Kane's 98 Premier League goals came in just 135 games for the club, 101 fewer than it took Sheringham to reach 97.
That was the end of the scoring as Spurs extended their unbeaten run against Everton to 11 games as the Toffees floundered to a sixth straight game without a win.
Kane's latest record comes after a stellar 2017 that saw the 24-year-old set a new record of 39 Premier League goals scored in a calendar year, beating the 36 that Alan Shearer managed in 1995. He can do everything because of his mentality, how he is as a professional.
"Harry can achieve all that he wishes to and all he wants to because it is unbelievable the way he is able to work and his willingness. He's always thinking and trying to improve, improve, improve and score goals".
"This is a historical tweet from many years ago so he [Holgate] doesn't need any reminding because all the players have already been made aware for more than this year".
Spurs should be good enough to secure a comfortable win here, and given Everton's struggles in front of goal, I can't see them getting past Hugo Lloris.
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. "It was massively worrying in terms of how can a performance become so bad in such a short period of time".
Spurs fans were pleased with the performance their side put in and took to social media to provide their reaction to one of their attacking players. 55' - Idrissa Gueye concedes possession in the centre circle and that allows Harry Kane to drive towards the Everton goal and get a shot away from 25 yards. He could have added more to tally too, having been denied by the woodwork and goalkeeper Pickford. The game continued to meander and it remained 1-0 at the break.