Everton had all the posession in the early stages, and Dominic Calvert-Lewin was one good touch away from being in on goal after a fantastic Idrissa Gueye pass.
However, West Ham shocked the hosts moments later, when Marco Arnautovic went through on goal, before squaring the ball to Andriy Yarmolenko. The Ukrainian tucked the ball past Jordan Pickford with composure.
The home side should have gone level after 25 minutes, when Cenk Tosun squandered a great cross from Lucas Digne by putting it straight at Lukasz Fabianski.
6 minutes later, West Ham doubled their lead when Yarmolenko scored a stunning second. After collecting the ball on the right wing, the 28-year-old threw off the attentions of Kurt Zouma with some fine stepovers, before curling a wonderful shot past Jordan Pickford.
September 16, 2018
Everton were revitalized when the game kicked off again, and for 15 minutes they bombarded the West Ham penalty area. It was easy to see why West Ham have struggled so far this season, and only Lukasz Fabianski repelled the waves of blue with a number of good saves.
However, the pressure finally told in added time at the end of the first half, when centre-back Jonjoe Kenny curled a perfect cross into the box. Everton captain Gylfi Sigurdsson rose well, and planted a firm header fast Fabianski in goal, giving his side a boost before half-time.
However, West Ham came out after the break a far more organised team, and they contained Everton well for the most part in a scrappy first 15 minutes.
However, after 61 minutes, Marco Arnautovic effectively killed the game. He linked up brilliantly with Pedro Obiang, before stabbing a shot into the bottom corner while off-balance.
It was a fantastic moment for the West Ham travelling support, only slightly marred by Arnautovic being forced off through injury 3 minutes afterwards.
Everton had plenty of posession from then onwards, but they couldn't make it count, as West Ham closed ranks and defended efficiently.
The only break in this pattern came in the 84th minute, when substitute Oumar Niasse thumped a volley from inside 10 yards against the underside of the crossbar. The Senegalese 28-year-old looked distraught, knowing that he should have at least hit the target.
From then, it was a simple matter for West Ham to close out the game and claim their first 3 points of the season, lifting them to 16th.
September 16, 2018
Everton remain in 10th, one place behind newly promoted Wolves.