That goal saw Kane equal Sheringham's tally and the England striker broke it 12 minutes later when he prodded the ball past Jordan Pickford from close range for his latest landmark display of the season.
Tottenham opened the scoring in the first half through Son Heung-Min, when he was able to stab home a Serge Aurier shot inside the penalty box.
They added a fourth goal with nine minutes remaining when Christian Eriksen rounded off an excellent attacking move from the London club.
Having already beaten Alan Shearer's calendar-year record for the most Premier League goals (39), the England worldwide also has two successive Golden Boots and has just equalled the all-time record for the number of Premier League Player of the Month awards, as his sixth has taken him level with Steven Gerrard.
The World Ends With You Returning On Switch
This modern take on the pure action platformer lets Madeline climb any surface on Celeste Mountain if she has the stamina. Debuting in the Nintendo Switch version of the game, a new playable character named Joy will be introduced.
Everton now sit ninth in the division but they have been woeful away from home having taken just 8 points from a possible 27 on the road so far this campaign.
Kane, the Premier League's top scorer with 18 goals and December's player of the month, recently suggested that Spurs have to start winning trophies if they want to retain his services amid reported interest by Real Madrid.
Cenk Tosun had a forgettable debut for Everton but if he is worth £27million - after scoring goals in Turkey - you have to wonder how much Son is worth.
Fifth-placed Tottenham moved to 44 points and are level with Liverpool who take on league leaders Manchester City on Sunday.
Harry Kane needs two more goals to reach his Premier League century.
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In an open letter earlier this week, YouTube said "suicide is not a joke, nor should it ever be a driving force for views". The news comes as YouTube released a statement confirming that Paul would be punished for his misdeeds.
He continued: "There are a lot of numbers, but he can do everything because of his mentality and how he is - he is so professional. He is always thinking to try to improve, improve, improve, score goals and improve for the team".
"What I can't excuse is out capitulation after we went 2-0 down".
He set a record of 39 Premier League goals in a calendar year in the process and has now joined the former Liverpool captain in the history books.
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. In this way he will break all the records in the Premier League.
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He finished with 98 yards from scrimmage on 17 touches, and LeGarrette Blount ran in the Eagles' only touchdown of the game. Nick Foles left the field in the fourth quarter after leading the Eagles to a game-securing field goal drive with the lead.