Kane's double took him to 176 Premier League goals and moved him above Arsenal legend Thierry Henry for sixth place on the all-time scorers' list.
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The writing had been on the wall for Everton long before then, though, in a wholly one-sided contest.
Under pressure from Son Heung-Min, Everton defender Michael Keane put the ball into his own net to start the scoring after 14 minutes. Son then scored himself three minutes later to propel a Tottenham team looking to bounce back from an FA Cup upset at the hands of Middlesbrough last time out.
After Kane added a third in the 37th minute, half-time substitute Sergio Reguilon extinguished any hopes of an Everton fightback less than a minute after the restart. Kane then soon applied the final flourish to take his total above Henry with a perfectly executed volley.
Kane is now just one goal short of Frank Lampard for fifth place on the Premier League top-scorers' list. The now-Everton manager has far greater concerns, however, on the evidence of this showing.
Everton have lost four of five league outings since Lampard was appointed to replace Rafa Benitez, leaving the Toffees just a point above the relegation zone.
Tottenham, meanwhile, will be looking up once again after an inconsistent run of form. Monday's win leaves them three points behind fourth-placed Arsenal in the battle for the final Champions League spot, although having played a game more.
"The top four has to be our ambition," Kane said afterward. "We are not the finished article yet but the manager has had time to settle in and physically, I think we are in a really good position.
"We are in there and in the mix and we have to feel that pressure if we want to be a top team."
Information from Reuters was used in this report.