The Tottenham striker broke Teddy Sheringham's record of 97 goals in the Premier League, making him the club's all-time scorer in the top-flight.
While Kane is not the only Tottenham player whose future is under scrutiny, the 24-year-old is arguably the most important player Spurs now have and his presence will define whether the North London side will enjoy success or not in the near future.
Son Heung-min put Tottenham ahead in the 26th minute, courtesy of another close-range strike, and produced possibly the highlight of the game with his spin and driving run to set up Kane's first goal.
Christian Eriksen then smashed in a fourth from the edge of the penalty area after a fine backheel from Dele Alli exactly nine minutes to stoppage time.
Kane remains well adrift of Spurs legend Jimmy Greaves's club tally of 220 goals in 321 First Division appearances - to the relief of manager Mauricio Pochettino.
Crystal Palace's Bakary Sako scored the only goal of the game in the 21st minute as Roy Hodgson's Eagles saw off Burnley 1-0 at Selhurst Park, while West Ham overpowered Huddersfield Town 4-1.
"He can do anything", Pochettino said. Sure. For me his quality, mentality and professionalism is top.
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But he says the loyalty of Kane, who has 125 Spurs goals in all competitions, makes him different to most modern players.
"I think we fully deserved the victory".
While Spurs maintained their recent surge in form, Everton slumped to their heaviest defeat under new manager Sam Allardyce. He said felt they could go attacking but he should have "gone back to being a bit more boring".
The second half is where Spurs kicked it up a notch.
"The disappointing thing for us is, what would the game have finished like had we scored the first goal when Wayne's got disallowed?" Obviously, it's something I have to address now. I saw some good signs of the players last week against Liverpool and I saw some of the worst signs in the second half today which is massively worrying.
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