Tottenham delivered a statement on the pitch and their joyous supporters made one off it. “He’s Tottenham, you know,” they sang of Mauricio Pochettino after humiliating Everton in their own back yard. Their coveted manager responded with a clenched-fist salute. Prospective job offers from Manchester United can wait. He may have a title challenge to consider first on this form.

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Pochettino’s focused team were outstanding as they inflicted the heaviest defeat of Marco Silva’s Everton reign to move within two points of Manchester City in second. Their reaction to the distraction of Old Trafford, both here and at Arsenal in midweek, has been flawless. It could haul them into the title race should it continue. Son Heung-min and Harry Kane both scored twice and led a comprehensive crushing that saw Everton outclassed. Silva’s side are without a win in five matches and have collected one point fewer than at the same stage of last season. Spurs, by contrast, are looking upwards and constructing a case for their manager to resist the anticipated advances from Old Trafford next summer.

It was a forgotten memory by the time Kane guided the visitors’ sixth goal past the overworked and struggling Jordan Pickford that both teams initially contributed to an open and compelling contest. The sheer quality of Spurs’ attacking play was a fundamental difference throughout, however. Everton were prised apart frequently by the pace and intelligent movement of Son, occupied by the power and quality of Kane and had no answer to Dele Alli’s ability to wreak havoc in the space he found behind their central midfield. Another costly mistake from Pickford and the decision to disallow a Dominic Calvert-Lewin header added to the home side’s miserable afternoon.

Facebook Twitter Pinterest Theo Walcott (left) opened the scoring for Everton but it was a miserable afternoon for the Merseyside club. Photograph: Chris Brunskill/Fantasista/Getty Images

The visitors created three excellent openings before falling behind to Theo Walcott’s first Premier League goal since August. Gylfi Sigurdsson, who provided Everton’s brightest moments, released Calvert-Lewin clear of the Spurs defence with a delightful backheel. He picked out the former Arsenal winger, who revelled in his close-range finish past Hugo Lloris. Calvert-Lewin and Walcott combined again moments later for what Silva claimed was a key moment in the game. The England Under-21 forward guided a superb header into the top corner but was adjudged to have pushed Davinson Sánchez by the referee, Paul Tierney. Spurs took full advantage of the reprieve. The speed of their passing, of Son, and their commitment to attack, obliterated Everton’s lead and their defensive composure. That said, they were gifted the way back by Pickford and Zouma.

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A first-time ball over the top by Kane sent Son on a hopeful chase. Zouma had the danger covered but Pickford decided to race out of his area and succeeded only in spreading confusion. The pair collided and from a difficult angle, Son floated a delightful finish into the vacant net. The South Korea forward was a class apart all game. Evertonians even joined in with the applause when he was substituted late on.

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The visitors’ gained the lead when neat, one-touch passing from Ben Davies, Moussa Sissoko and Alli released Son on the left. Pickford saved the striker’s low shot with a strong left hand but the ball fell invitingly for Alli to drill the rebound home. It was three before Everton could regroup at the interval. Son was again involved, winning a free-kick that Kieran Trippier whipped against Pickford’s left-hand post from 25 yards. The rebound fell Spurs’ way once more and Kane gratefully converted with the goalkeeper grounded.

Pickford was extremely fortunate to escape punishment for a rash challenge on Alli that led to his England teammate’s departure at half-time with a hamstring injury. Alli had been given offside when the keeper committed the foul.

Facebook Twitter Pinterest Dele Alli was on the end of an ugly tackle by Jordan Pickford just before half-time. Photograph: Jan Kruger/Getty Images

Christian Eriksen swept a beautiful half-volley beyond Pickford within minutes of the restart, crushing any hope the home side entertained of a recovery. Trippier released Kane down the right, as in the first half, and though Séamus Coleman headed the striker’s cross clear he was powerless to stop the return from the Danish midfielder, a controlled, precise finish that flew into the bottom corner.

Sigurdsson reduced the deficit with a fine finish of his own, collecting a pass from Richarlison and evading four weak challenges in a mazy run across the area before cutting his shot back beyond Lloris. But there was never any prospect of an Everton recovery. Spurs claimed their fifth when Érik Lamela, Alli’s replacement, dissected the home defence with a piercing pass that sent Son clean through on goal while Everton appealed in vain for offside. The striker shot through the legs of Pickford and then delivered the assist for Kane’s second of the game with a low cross from the left. Kane opened his body and diverted a textbook finish wide of the exposed Pickford. The rout was complete.