Kane looped the ball over Everton goalkeeper Jordan Pickford from the far right to open the scoring in the 28th minute and playmaker Christian Eriksen scored the second goal from close range after Everton failed to clear the ball in the 42nd minute.
Twenty-four-year-old Kane scored his second of the match from a Ben Davies cross at the beginning of the second half as Tottenham continued to outpace a limp Everton side and created a host of chances but fine saves from Pickford denied them.
"I think it was a fantastic performance. We played very well. We are so pleased and I congratulate the players," Tottenham boss Mauricio Pochettino said.
Tottenham goalkeeper Hugo Lloris was largely untroubled throughout the game as Everton managed to get just one of their 12 shots on target while six of Spurs' 15 efforts were on target.
"I am disappointed ... but after the lucky 1-0 down it was really difficult. We lost control in the game. Tottenham's midfield diamond was difficult to control," Everton manager Ronald Koeman said.
"The frustration is the second half ... We were too nice, too weak in the second half, but that is also something about confidence.
"The key is to learn from today."
The defeat dropped Everton to 15th in the table and they could slip further depending on Sunday's results, while Tottenham climbed to fifth, a point behind fourth-placed Watford.
The Merseyside club have failed to beat Tottenham in their last 10 league meetings and their tough start to the season continues when they travel to Manchester United on Sept. 17, with Tottenham hosting Swansea City the day before.
(Reporting by Aditi Prakash in Bengaluru; Editing by Clare Fallon, Neville Dalton)
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