Goals from Son Heung-min and Christian Eriksen either side of Kane's brace meant Spurs are now level on points with Liverpool in fourth place despite their poor run of form earlier in the season.
Mousa Dembele returned for Spurs, whilst Everton's £27m signing Cenk Tosun started up front as the Toffees got their first chance to look at the man who they hope can replace Romelu Lukaku.
The opening exchanges consisted of both sides passing the ball sideways with no real intent to create chances, and the chances that came later were all one way as Hugo Lloris wasn't forced to make a save all game.
Kane will take all the plaudits as usual but Son ran this game for Spurs— Khalid (@WorldOfK_) January 13, 2018
Wayne Rooney had the ball in the back of the net seven minutes later but it was ruled out for offside. Tosun headed the ball to the back post where Rooney had peeled off just a tad too early
Spurs opened the scoring in the 26th minute when Eriksen's beautiful cross-field pass to Serge Aurier split the Everton defence in half. The Ivory Coast international was afforded far too much time and space to pick out a low driven cross for Son to tap in and equal
Harry Kane bags his 20th league goal of the season, reaching that landmark for the fourth successive season, and has now scored 10 goals in his last 7 appearances for Tottenham at Wembley #TOTEVE— WhoScored.com (@WhoScored) January 13, 2018
Spurs came steaming out of the blocks for the second-half though and doubled their lead two minutes later. Son did brilliantly down the left hand side and his low cross was flicked in by Kane.
They were really starting to turn the screw and almost had a third five minutes later. Dele Alli and Son played some wonderful passes between each other to set the England international one on one with Pi
What. A. Goal. — Joe Prince-Wright (@JPW_NBCSports) January 13, 2018
Kane to Aurier to Son to Dele and a lovely back heel to Eriksen to finish. One of the best team goals you will see this season. #THFC absolutely flying.#TOTEVE 4-0 pic.twitter.com/XP7eECDz4i
And that was how the match finished. Everton lose their opening three matches of a calendar year for the first time since 1960 while Spurs continue to march up the table in an attempt to snatch a Champions League place.