The only slight surprise was that he didn’t extend his astonishing recent scoring streak of 10 goals in his last six matches by collecting his first hat-trick of the New Year.
What was equally odd 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.
Sharpened by a week’s break between matches after the December logjam of games, the home side showed off their crisp passing without forcing any clear-cut chances early on.
That changed in the 15th minute when an Idrissa Gueye trip on Dele Alli gave Tottenham a free-kick. Christian Eriksen speared it in and Son Heung-Min’s flicked back header looped just beyond the far post.
The former England captain thought he had scored after 22 minutes, nipping past his marker to nod in a Tosun header from an Everton corner only to see the raised offside flag.
This time it was Tottenham’s turn to respond immediately. Three times in as many minutes, Harry Kane forced saves out of Pickford with shots from the edge of the area.
The opening goal came from a different source. Eriksen’s cross-field pass found Serge Aurier with space to attack. Having done so, he tried a shot which skewed across the six-yard area and perfectly into Son’s path for an easy tap-in.
The remainder of the first half was high on technical excellence if short on excitement. The only moment of note came on the stroke of half-time when Phil Jagielka earned himself a booking with a body check on Alli.
It took just two minutes of the second half for the game to spring back into life. Clearly relishing his full-time role this season, Son pirouetted his way past Mason Holgate 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 with an exquisite short pass only for Alli to send 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 after Son had combined with Alli, who smartly backheeled the ball into the Dane’s path.