José Mourinho celebrated with a knee-slide and it was the moment when his Tottenham tenure felt up and running. The club’s new manager had wanted to see the real Dele Alli, not the midfielder’s brother, and when he did the emotion came pouring out. What a piece of skill Alli produced in the 43rd minute and it not only got Spurs away for Lucas Moura to make it 2-0, it killed a West Ham team who look to be in freefall.

West Ham United v Tottenham Hotspur: Premier League – as it happened Read more

Alli had stretched to keep in a heavy Eric Dier pass on the left touchline and slipped over but, lying on his back, he fashioned a flick with the inside of his right heel that moved the ball under his body and released Son Heung-min to make the assist. Alli’s move would not have looked out of place in a football freestyler’s clip on YouTube and, according to Mourinho, was the mark of a player in “focused and ultra confident” mood. “Dele is too good not to be one of the best players in the world,” he added.

Mourinho had stressed that his work at Spurs in the aftermath of succeeding Mauricio Pochettino would be a process but this was an encouraging start, albeit against a feeble West Ham, who have taken two points from seven matches. Son got things started with the first goal, Harry Kane scored the third and it added up to Spurs’ first away win in the Premier League since January; the breaking down of a mental barrier.

For West Ham, the problems seemed everywhere, although they began in goal with Roberto – a figure to spread panic rather than calm. It was not a good look when the home crowd cheered him ironically in the 80th minute when he made a clean catch. West Ham did fight until the end and, as Spurs tired – partly because of the psychological strain of the managerial change, in Mourinho’s opinion – the hosts cut the deficit.

The substitute Michail Antonio tricked Toby Alderweireld before finishing smartly and Mourinho would have winced at some of the Spurs defending in the closing stages. Declan Rice had a stoppage-time goal ruled out for offside by VAR and Angelo Ogbonna scored with the last kick of the game from a Robert Snodgrass corner. But the grandstand comeback had never felt on for West Ham; the goals merely papered over the cracks.

Facebook Twitter Pinterest José Mourinho reacts after Spurs’ third goal as Manuel Pellegrini looks on. Photograph: Tom Jenkins/The Observer

What Mourinho would do with his lineup and tactics provided one of the subplots and his 4-2-3-1 system featured Dier in defensive midfield and no Christian Eriksen at the outset. Mourinho said he loved his team’s football for the first hour, even if they were a little error-strewn early on, and perhaps the biggest shift from the Pochettino years was the lack of playing out from the back. Spurs were more direct and fought for the second balls.

Son bristled with menace on the left, despite catching one bad challenge from Ryan Fredericks, and his goal followed an Alli pass. It was all too easy, with West Ham’s players guilty of standing off, and it was far from being the only time their defending could be criticised. Son executed a simple shimmy and, rather abruptly, Issa Diop was a yard away from him, with the shooting chance on. Son banged it low and hard, and it almost seemed to go through Roberto.

The second goal was the show-stopper, leading to Mourinho’s delight, but Spurs had the opportunities to score even more before the interval when West Ham were booed off, having done little in the final third.

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Kane found the net early on from Alli’s pass only for an offside flag to deny him while Davinson Sánchez almost profited when Roberto dropped the ball into him following a free-kick. Roberto also saved from Son and Sánchez.

Manuel Pellegrini made all three of his substitutions by the 64th minute as he groped for the solution but his decision to replace the hapless Diop with the unpopular Carlos Sánchez and ask Rice to drop into central defence was jeered.

Spurs were in complete control for the first half of the second period, with Moura wasting a glorious chance on the break, but Kane’s goal would come shortly afterwards – a firm header from Serge Aurier’s cross. Where was his marker, Diop? The resigned silence of the West Ham crowd for long spells spoke volumes.

Kane, who was on the end of some rough treatment, almost got away from Diop for another goal on 61 minutes and West Ham’s late push probably served to dilute the strength of the boos at full-time. Pellegrini is under increased pressure whereas Mourinho, back in his “natural habitat”, could enjoy the sound of the music in the dressing room afterwards. He has something to build on.