Tottenham Hotpsur’s unbeaten run remains intact but of far more importance to Mauricio Pochettino after this classic encounter will be that his team’s seven-game winless streak has ended. Spurs dominated for long spells of this pulsating London derby but they needed Harry Kane, the most prolific of scorers in inter-capital fixtures, to strike twice in the final two minutes to transform a maiden defeat of the season into their first victory since 2 October.

West Ham had led twice, through Michail Antonio’s first-half goal and Manuel Lanzini’s 68th-minute penalty after Harry Winks made it 1-1 with a goal in his first league start, but a defensive substitution from Slaven Bilic five minutes from time proved desperately costly for the visiting team. They remain 17th and face a daunting set of fixtures, making their inability to close out the win all the more frustrating.

Yet the real story was how Kane, who is still working his way back to full fitness, scored twice to overturn the deficit. The first came after Son Heung-min’s cross was parried by Darren Randolph into the England striker’s path before a minute later Son was tripped by Havard Nordtveit in the area, giving Mike Dean no option but to point to the spot. Kane drilled it into the bottom left corner from 12 yards.

Bilic had introduced Nordtveit only six minutes earlier for Dimitri Payet, at a time when the France attacker was looking menacing on the break. Such a conservative change invited Spurs on and West Ham duly crumbled, with Nordtveit deserving much of the blame.

“It looked good for us,” Bilic said. “Especially after the goal we scored, but we had good opportunities to kill the game off. Unfortunately it wasn’t to be.”

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However, one had to marvel at the drive displayed by Spurs. Pochettino reckoned they were “sloppy” during the first half, yet their self-belief did not wilt and with Kane on the pitch there was always a route to goal.

His tally in derbies is now 18 from 22, the best ratio of any striker in the Premier League era. “He’s back,” Pochettino said. “For me he’s one of the best strikers in the world and I’m very, very happy with his performance.”

Considering the history between these two, it was always going to be an exception to the unwritten rule that games immediately after the international break take time to ignite. Both were hungry to claim an early foothold and although Tottenham monopolised possession for much of the opening 45, Randolph had very little to do.

Pochettino’s decision to pair Kane with Vincent Janssen, believing two strikers would work best against West Ham’s three-man defence, did not work initially and Spurs were left short in wide areas when being countered.

In saying that, Antonio opened the scoring from a set piece. The wing-back had an initial effort blocked by Kyle Walker and from Payet’s corner Cheikhou Kouyaté’s header came off the bar. The rebound broke to Winston Reid, whose attempt took a heavy deflection and Antonio was in the right place to head past a scrambling Hugo Lloris from close range. It was his sixth goal of the season and all have been headers.

Facebook Twitter Pinterest Michail Antonio gives West Ham the lead in the first half at White Hart Lane. Photograph: Andrew Matthews/PA

As half-time approached Pochettino grew exasperated with Tottenham’s lateral play and was apoplectic in the opening minutes of the second period when Mousa Dembélé dawdled under a high ball, allowing Diafra Sakho to muscle in and intercept. He fed Payet, who cruised goalwards but was halted by a terrific tackle from Jan Vertonghen.

Those frustrations were soon relieved when Winks tapped home at the conclusion of Spurs’ first proper flowing move of the evening. Danny Rose advanced speedily down the left and found Janssen at the near post. His shot was parried to the feet of Winks, who tucked home.

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There was no mistaking the added purpose to Spurs’ football at that point and only a brilliant Randolph save to deny Eric Dier stopped them from taking the lead just before the hour. Yet completely against the run of play West Ham retook the advantage when Janssen had his arm around the shoulder of Reid from a corner and Dean immediately pointed to the spot. Lanzini sent Lloris the wrong way.

It was all going well for the Hammers but when Payet, their main creative outlet, was removed it became a backs against the wall job and eventually the pressure told – to such an extent that Reid was booked twice in injury time and will now miss Sunday’s trip to Manchester United.

“We were better than West Ham,” Pochettino said. “One team deserved to win the game and it was Tottenham, no doubt. But we can do better.” An ominous sign before Tuesday’s Champions League game at Monaco.