The forward opened his account for the season with an effort that was an attempted cross from the right but looped over home keeper Jordan Pickford.
Christian Eriksen scored Spurs’ second from close range before Kane sealed the game with a neat finish 47 seconds after the break.
In truth, it could have been have ended 6-0 to a totally dominant away side.
Tottenham’s win takes them to seven points and propels them back up the table to fifth.
For Everton, after their loss at Chelsea in their previous game, this is another chastening defeat against a top-four side they aspired to match following a summer of heavy spending in the transfer market.
After finishing second last season, Tottenham have been somewhat inconsistent at the start of this one, winning comfortably away at Newcastle but then dropping points at home as they continue to find their feet at Wembley.
However, this performance, against a side with lofty aspirations of their own, shows that they once again mean business and that the consistency of their starting XI over the last three campaigns brings with it a fluency unrivalled by most in the division.
Once Mauricio Pochettino’s side had found a foothold in the game, Everton were unable to get a look in. Kane’s second goal essentially killed the contest, but it may as well have been over from the moment his first found the net.
Kane will rightly take the headlines, but this was a team performance, with Eriksen the creative force, topped by his own first goal of the season – a close-range finish after Pickford had palmed out Ben Davies’ shot.
The Dane played in front of a back three made that much more assured by the presence of summer signing Davinson Sanchez.
Before the three goals, Eriksen fired wide and Moussa Sissoko had a goal-bound effort blocked in the box.
After them, an unmarked and central Dele Alli air-kicked a cross from Kane, who later pulled a shot wide from inside the box.
The 3-0 scoreline was more flattering to Everton than Spurs.
