For Harry Kane, the records continue to tumble and the reality was there was never any doubt. Another day, another hat-trick. It was the Tottenham Hotspur striker’s eighth of 2017 but the headline details were even more eye-catching.

Kane had Alan Shearer’s Premier League mark for a calendar year in his sights and he duly overhauled it. Shearer scored 36 times for Blackburn Rovers in 1995; Kane has finished the year with 39 and he did it from 36 matches. Shearer took 42.

Even better for Kane is that he now stands as Europe’s leading scorer from 2017 – ahead of Barcelona’s Lionel Messi, the player that he one day hopes to supplant as the best in the world. Messi has 54 goals from 63 appearances in all competitions. For Kane, it is 56 from 52.

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It was an occasion when the atmosphere was slightly subdued, despite the excellence on display, and it was easy to imagine the bloated insides and fuzzy heads in the stands. Kane’s clarity of purpose shone brightly. He opened up with a header before dispatching two left-footed efforts and he is now the top scorer in this season’s Premier League with 18. Nobody would bet against him adding a third consecutive Golden Boot.

It was a miserable 90 minutes for Southampton and their manager, Mauricio Pellegrino, who heard chants from the travelling support about him being sacked in the morning. Once again he started without Virgil van Dijk in his squad – it seems inevitable the defender will get the move he has pushed for in January – and it is now seven games without a win for the club.

Pellegrino’s team were dreadful in the first half but at least they kept fighting when the game was over at 4-0. Sofiane Boufal got their first consolation goal when he beat Hugo Lloris for power at his near post, while Dusan Tadic scored the second after further uncertainty from the Tottenham goalkeeper. Pellegrino said the bad period would show him “how people really are – who are the players that want to fight 100% for the club”.

Dele Alli was impressive for Spurs, scoring one, setting up two and having a prominent role in another, while Son Heung-min also got himself on the scoresheet. But this was a game that was all about one man.

Kane could and should have had more. He touched wide from Christian Eriksen’s low cross on six minutes but he did not have to wait long for the goal that took him past Shearer and level with Messi. The opportunity might have come from the penalty spot but Pierre-Emile Hojbjerg’s foul on Danny Rose was just outside the area on the left-hand side. When Eriksen stood over the free-kick the alarm bells continued to sound for Southampton.

The delivery was superb, bent into the corridor between goalkeeper and backline, although it was still easy to wince at the marking. Kane was more than a yard in behind Wesley Hoedt and Oriol Romeu was hopelessly on the wrong side. Kane’s header flashed home.

Southampton offered next to nothing in the first half but they almost found a way back into it via an unlikely source. Lloris flapped at Boufal’s shot, pushing it up and out and what happened next seemed to unfold in slow motion. Rose put too much on his attempted back header and it looked set to loop over Lloris for an own goal. The keeper, though, got something on to it, raced back and patted the ball on to his post before clutching it gratefully.

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Back to Kane. He banged a free-kick into the wall and popped another shot high from 25 yards. The striker terrified Southampton every time he picked up possession and there was a lovely crossfield pass from him on 42 minutes that released Son. Jack Stephens did just enough to force the South Korean off balance without conceding a penalty.

By then Kane had scored his second and it was a beautiful team goal, embossed by the flair and vision of Alli. The midfielder collected Eriksen’s pass and took two defenders out with a spin and then a third with a slide-rule pass for Son. He crossed low. You-know-who swept home.

Kane might have completed his hat-trick in first-half stoppage time. After Eriksen’s flick, the chip from distance was on for him and it said everything that you half-expected him to execute it. He could not.

Southampton flickered at the beginning of the second half. Shane Long almost got in after Eric Dier’s mistake while Mario Lemina rattled the crossbar from the edge of the area. But no team can defend as badly as Southampton did and expect to emerge without heavy damage.

Alli got the goal that his performance deserved after he picked up possession on the left-hand edge of the area. With no challenge forthcoming, he sauntered inside and shaped a low right-footed curler into Fraser Forster’s far corner. Son’s goal followed shortly afterwards and it owed much to Alli’s pace on the counter-attack, not to mention the timing of his pass. Son’s finish was clinical.

Kane grazed the outside of the far post with a volley from Rose’s crossfield pass on 57 minutes and the hat-trick finally came after another quick break and Alli assist. Maya Yoshida looked tired as he tried to get close to Kane, who clipped coolly over Forster.