These days a team is not really a Premier League side until Harry Kane has shattered their defence. So this was an initiation of sorts for Huddersfield Town, who became the latest victims of a striker whose goals are fuelling Tottenham’s trophy ambitions and his own quest to break records.

David Wagner’s team had conceded only three goals in their first six top-flight matches since promotion but Tottenham fired that many past them in the first 23 minutes here, with Kane, inevitably, leading the onslaught. He scored the visitors’ first and third goals, and was instrumental in creating the second for Ben Davies. The left-back Davies helped the visitors add a fourth in stoppage time by setting up Moussa Sissoko.

Kane now has 84 goals from 123 Premier League appearances. And his strike rate is accelerating: factor in his midweek hat-trick in the Champions League against Apoel Nicosia and he has hit 13 goals in all competitions in September, the most productive month of the 24-year-old’s career to date. Mauricio Pochettino is almost lost for words.

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“It’s difficult to speak every three days about Harry Kane and find different words to describe him,” the Tottenham manager said. “He’s great in front of goal. And when we don’t have the ball he is the first to run and fight for it. He’s a very good example for football. So humble. It’s so lucky for us a to have a player like him.”

Kane tried to open the scoring here in the second minute but saw his shot deflected behind by Mathias Jorgensen. Then Huddersfield had the temerity to try to get on the scoresheet before him, Hugo Lloris thwarting a shock by diving full-length to tip away a powerful long-range effort by Tommy Smith. Then Kane took over.

He had unwitting help from Huddersfield’s left-back Chris Löwe, whose mistake on half-way turned a banal clearing header by Kieran Trippier into the perfect through-ball for Kane. The striker did the rest, cantering forward and into the box before finishing as matter-of-factly as a librarian slotting a book into the correct space on a shelf.

Löwe was unfortunate to play a role in Spurs’ second, too. That came seven minutes later after snazzy interplay down the left between Dele Alli and Kane, who flicked a pass through to Christian Eriksen at the edge of the area. Löwe poked the ball off the Dane’s foot but when it ran across to the other side of the box, Davies lifted it over the advancing Jonas Lössl with a delicate finish.

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With Spurs seemingly intent on punishing every error, Lössl must have feared the worst when he miskicked an attempted clearance and thus gifted the ball to Kane. But the goalkeeper recovered sufficiently to rob the ball back. However, the relief was only temporary. In the 23rd minute Kane struck again, rolling past two opponents before curling a precise left-foot shot into the net from 20 yards. “He’s just a one-season wonder,” chanted the away fans with gleeful sarcasm.

Spurs were a class above anyone Huddersfield have encountered so far this season. This was the fourth away match in a row in which they have struck three goals, and they could have increased the tally before half-time. Alli struck the post after one smooth move down the right.

Huddersfield, made to look ragged at times, did not bow down. Laurent Depoitre cracked a ferocious long-range shot against the crossbar just before the break.

The home side tightened up in the second period, determined not to permit a tonking. Christopher Schindler hurled himself in front of a shot to prevent Kane plundering another hat-trick. Alli darted through the defence in the 57th minute but when he collapsed in the box as Lössl came to challenge him, the referee booked him for diving. He had been rumbled. “If it was [a dive], he must learn because this type of action doesn’t help him, doesn’t help the team and doesn’t help football,” said Pochettino. “We’ve talked in the last few years about fair play and being honest. I think he’s improving a lot but it’s still something he has to learn.”

Spurs did not over-exert themselves after that, knowing the game was up for Huddersfield. But Sissoko scored in stoppage time, anyway, bundling the ball into the net after a charge down the left by Davies.

Kane had been substituted by then, leaving in the 86th minute to applause by supporters of both clubs. This was Huddersfield’s first meeting with Tottenham since 1972 and they have still not beaten the Londoners since 1956, when they had a player in their team, Ray Wilson, who would later win the World Cup with England. Here the Yorkshire team were shot down by another Englishman who could go on to greatness.