The only slight surprise was that Kane was not the player who stood out most in a white shirt. That honour belonged to Son Heung-Min, who bestrode the match with an astonishing display.
It was all too much for Everton, who floundered on the road once more in spite of giving a debut to Cenk Tosun, their recent £27m signing from Besiktas.
Tottenham manager Mauricio Pochettino said: “I’m very happy. I thought the performance was amazing and I congratulate Harry one more time.
“He can achieve all that he wants because of his willingness to work. He’s always thinking and trying to improve, improve, improve and score goals.
“It was a great performance from Son today, but it’s not only today. He has been like that for one, two, three months. He is more mature than last season and his level, belief and his confidence are showing more in every game. It is fantastic.”
Harry Kane’s best goals of 2017
The opening 20 minutes were characterised by Tottenham’s crisp passing, yet it was Everton who almost took the lead.
Wayne Rooney thought he had scored, nipping past his marker to nod in a Tosun header from an Everton corner only to see the raised offside flag.
Tottenham responded immediately with Kane forcing Jordan Pickford into saves three times in as many minutes.
They went ahead when Christian Eriksen’s cross-field pass found Serge Aurier, who burst forward but skewed across the six-yard area and perfectly into Son’s path for an easy tap-in.
If the remainder of the first half was high on technical excellence and short on excitement, the game sprang back into life just two minutes into the second period.
Clearly relishing his full-time role this season, Son pirouetted his way past Jonjoe Kenny on the halfway line before driving forward and laying the ball perfectly beyond Pickford’s reach and into Kane’s path. Of Kane’s 32 goals this season, it was surely the easiest.
It also settled this match as a contest. With the score at 2-0, an intriguing sub-plot raised its head. If Everton were to concede another three goals, they would see Tottenham overtake their Merseyside rivals Liverpool.
Son and Kane were clearly in the mood to achieve exactly that. First, Son picked out Alli, who sent his shot into the side netting.
Next, Son took the responsibility himself with a fiercely struck low shot which thudded against the base of the post.
Finally it was Kane – who else – who made sure of adding a third, easing in front of his marker to turn home an Eric Dier pass. Whether by design or accident, the ball looped over Pickford and dropped over the line beyond.
Tottenham kept surging forward and it was Eriksen’s turn to score their final goal, sweeping home after Son had combined with Alli, who smartly backheeled the ball into the Dane’s path.
Everton had been dismantled away from home once more, much to the dismay of manager Sam Allardyce.
Saturday’s Premier League matches in pictures
He said: “It was a shocking second half performance. I saw some of the good sides of the players last week against Liverpool and I saw some of their worst sides in the second half today, which is massively worrying.
“I might have a bit of responsibility to take by playing too many attack-minded players, but I can’t excuse our capitulation after we went 2-0 down.
“Obviously it’s something I have to address now. I didn’t expect to see it. I’ve seen it and now I have to address it as quickly as possible.”