Kane grabbed Spurs' second goal just after the break as he latched on to Heung-min Son's cross, finishing from close range.
Christian Eriksen finished off a sweeping move on 81 minutes to round off a comfortable win.
Spurs got their tactics spot on to avoid being frustrated by Everton because this game threatened to be quite tedious - although it proved to be not the case.
Tottenham Hotspur's Harry Kane celebrates scoring his side's third goal of the game during the English Premier League soccer match Tottenham Hotspur versus Everton at Wembley Stadium, London, Saturday Jan. 13, 2018.
According to the Daily Mail, there are 34 Premier League players who are earning more than the 24-year-old, including West Ham's Javier Hernandez (£115,000 per week), Crystal Palace's Christian Benteke (£120,000 per week) and Liverpool's Daniel Sturridge (£150,000).
"I'm so happy because these points give us the belief and confidence to fight with Chelsea, Liverpool and Manchester United for a place in the top four".
Tottenham took the lead four minutes later with Son tapping Serge Aurier's cross into the net.
The striker is the league top scorer with 20, three more than nearest rival Mohamed Salah.
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On a positive note, Idrissa Gueye is fit and available for selection, as is striker and latest club signing Cenk Tosun, who has arrived from Besiktas for a rumoured £27 million fee. Other than a disallowed Wayne Rooney goal, who was clearly, albeit marginally offside, the Toffees couldn't muster anything threatening going forward against a spry Spurs unit.
There are not many thing Kane has failed to do for Spurs in terms of scoring - but one thing is score in five successive Premier League home games.
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 looking to improve and that's what makes him special".
"I thought we had cut that out, so for me it is about making the players understand that it has happened once, in the second half - it can not happen again".
"I think Tottenham is a club that in three and a half years I've seen a minimum of 100 names linked and in the end we sign a few".
Sam Allardyce: "Maybe I have a bit of responsibility by playing too much attacking-minded players and not as many defending-minded players".
Saturday's final game sees Tottenham host Everton in a game that both teams desperately need to win.