With media duties over and free to commence birthday celebrations, Manuel Pellegrini was asked what West Ham’s players had given him for his 65th. “Three goals,” he beamed. They gave him so much more: a first Premier League win of the season, a release from the pressure and a performance to dispel the doubts that had developed in the early weeks of his reign, to be precise.

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West Ham’s losing run felt like a trick of the mind as they confidently condemned Everton to the first defeat of Marco Silva’s tenure and executed Pellegrini’s pre-match instructions to perfection. “I told the players that Everton must feel from the start that we have come to get three points, not just have a good performance,” the Chilean said. In Andriy Yarmolenko and Marko Arnautovic the visitors possessed the quality necessary to punish an error-strewn Everton performance and disorganised defence. Yarmolenko struck twice on his full league debut to demonstrate his fitness is improving in tandem with West Ham’s appreciation of their new manager’s ideas. Arnautovic added a merited third before departing with a knee injury that will be assessed on Monday.

Even accounting for several notable absentees in the Everton ranks the manner of West Ham’s win confirmed four consecutive defeats had left no lasting damage on team morale. By contrast this was a weak and worrying display for Silva, littered with individual errors from Jordan Pickford in goal to Cenk Tosun in attack. Everton started crisply but, without the suspended Richarlison, they lacked threat and balance. It was they, not the team who started the day at the foot of the table, whose confidence shattered with the first telling mistake of the game.

“We didn’t perform to a level to win this match,” said the Everton manager, who has overseen a mediocre start at Goodison Park. “I already told our players that at this level you cannot make mistakes like we made and when you create chances you have to score. After the first mistake we didn’t react like we had to react and the game changed completely. We lost our confidence.”

Yarmolenko was in the mood to punish Everton’s catalogue of mistakes. The Ukraine international, one of six changes made by Pellegrini, once helped Dynamo Kyiv dismantle Roberto Martínez’s Everton in a Europa League tie and was a transfer target for the Goodison Park club before moving to Borussia Dortmund. The 28‑year‑old gave Everton further cause for regret by sweeping West Ham into a comfortable first-half lead. His opener came after Tosun was brushed off the ball by Fabian Balbuena. Pedro Obiang released Arnautovic clear of a chaotic Everton defence – one missing Séamus Coleman, Yerry Mina, Phil Jagielka and Michael Keane through injury – and the Austria international selflessly squared with only Pickford to beat for Yarmolenko to convert from close range.

Everton were static, careless and posed minimal threat as they served a reminder that last season’s failings will not be eradicated easily. They were two goals down when Pickford, under no pressure, pinged a clearance straight to Mark Noble with his defence exposed. Noble released Yarmolenko on the right and the winger was invited to cut inside by Kurt Zouma, duly accepted, and curled an unstoppable finish beyond Pickford. Everton’s keeper punched the pitch in frustration, as well he might.

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It was only when Silva changed Everton’s shape to match West Ham’s three-man midfield that the home side improved. The summer signing Bernard replaced Morgan Schneiderlin, playing after the death of his father in midweek, and improved the energy and distribution from the home midfield immediately.

Seconds before the break Gylfi Sigurdsson rose impressively to head Jonjoe Kenny’s inviting cross beyond Lukasz Fabianski and Everton were spared the half-time jeers. Tosun should have done so earlier when Lucas Digne’s cross found him unmarked in the area but, at full stretch, he headed tamely at Fabianski. The West Ham keeper also saved from Theo Walcott’s volley in what was a rare moment of danger for the visitors.

The timing of Sigurdsson’s goal offered unexpected hope to Everton. Other than an optimistic penalty claim when the goalscorer was shouldered aside by the influential Obiang, however, the prospect of a comeback was remote. It became non-existent when Arnautovic restored West Ham’s two-goal advantage just after the hour.

Once again Everton applied minimal pressure on the ball as Obiang twice exchanged passes with the lone striker – despite having five royal blue shirts around him on the edge of the area. The midfielder’s second ball was perfectly weighted for Arnautovic to convert under Pickford.

Tosun missed another good chance while his replacement, Oumar Niasse, volleyed against the crossbar but there could be no denying West Ham a belated and well-deserved first Premier League win. Slowly they are adapting to Pellegrini’s methods.