Predictions have been pretty pointless so far in this topsy-turvy Premier League season but much more of this and people are going to start backing Tottenham Hotspur for a Champions League finish.

After the encouragement of the performance, if not entirely the result, in the 1-1 draw at Arsenal before the international break they swatted aside a West Ham team who have made a habit of rousing themselves for the big away games.

Not here. Apart from a decent enough opening 20 minutes Slaven Bilic’s team were second-best in all areas - particularly defensively - and it was hard to think of any of his players who truly shone.

Tottenham revelled in a victory over their rivals that extended their unbeaten run in the Premier League to 12 matches - a club record. The goals are flowing once again for Harry Kane and the two here made it eight in his last five club appearances. He has scored in his last four league games; Jamie Vardy, watch out.

The White Hart Lane crowd said they wanted five after Kyle Walker had played a give-and-go with Son Heung-min to bang home the fourth with the outside of his right boot for his first goal since December 2013 and it was one of those days when virtually everything went to plan.

The only disappointment for Tottenham was the needless booking that Dele Alli picked up after he became embroiled in a row with Mark Noble that had not really concerned him. Alli stepped in to defend Kane, his team mate, and he will be suspended for next Sunday's home game against Chelsea.

It was Tottenham's intensity, the ferocity of their collective work and their decisiveness that stood out. They squeezed the life out of West Ham whose only response was the late consolation from Manuel Lanzini, a wonderful strike that deserved more than the status of a foot-note. Lanzini turned Walker inside then out before lashing into the roof of the net.

West Ham had arrived on the back of their best Premier League start having won all three of their previous London derbies this season and with a positive recent record at this stadium. But they unravelled after Kane had opened the scoring and they could have suffered a much heavier defeat.

It was always going to be a battle to earn the right to play with space at a premium in the early stages and both teams keeping men behind the ball. Mauricio Pochettino could be seen urging his Tottenham players to press higher and higher.

It was his team that won the right, West Ham who blinked first, and then again and again. Adrián had repelled Christian Eriksen's left-footed drive, which took a slight deflection off James Tomkins, when Tottenham went ahead. Bilic could be deeply unhappy with his defenders at various points of the afternoon and the first instance was Carl Jenkinson's failure to keep hold of Kane.

Son worked the ball to Alli and the midfielder’s shot was blocked before it squirted back off him to break for Kane. It was crowded and messy inside the area and Jenkinson appeared to have the position on Kane. But the striker used his strength to roll away from him and thrash a shot high past Adrián.

Bilic barely flinched when Tottenham's second went in. Instead, he stood and stared at the carnage that Toby Alderweireld had wreaked inside the West Ham box. It was not difficult to read behind his stony features. From Eriksen's corner Alderweireld got the jump on Winston Reid with a quick dart towards the near post and when the West Ham defender passed him on to Andy Carroll, the alarm bells were ringing. Alderweireld rose in front of Carroll to flash his header home from point-blank range.

Tottenham might have had more before the interval. Son threw West Ham’s defenders with a drop of the shoulder before working Adrián and, on the follow-up, Alli put his head in front of Tomkins’ high boot to loop an effort against the crossbar. The clearest chance of the first half fell to Kane on 39 minutes, after a ricochet off Reid but one-on-one with Adrián he dragged his left-foot shot badly.

West Ham lamented the moment at 1-0 when, after Noble’s shot had looped up and the offside flag mystifyingly, stayed down, Cheikhou Kouyaté leapt into an overhead kick and crashed it against the crossbar. Kouyaté was also close to getting a touch on Carroll’s downwards header following a corner.

But Tottenham turned the screw in the second half and Kane’s third followed West Ham’s most excruciating lapse. Tomkins, attempting to play out from the back, rolled the ball straight to Eriksen who shifted it quickly up to Kane. His low shot flicked off Reid and fizzed underneath Adrián, who had to do better.

Adrián was actually West Ham’s best player and he made a fine double save to deny Son and Eriksen in the 53rd minute. There was plenty of niggle, with Walker and Diafra Sakho getting booked later on. Tottenham enjoyed themselves and they might have got the fifth only for the substitute Ryan Mason’s long-range shot in the last minute to hit the post. Guardian Service