It took 28 minutes for the first effort on goal and recalled Everton goalkeeper Maarten Stekelenburg saved comfortably from Havard Nordtveit's shot from outside the box.
West Ham: Adrian, Fonte, Reid, Collins, Kouyate, Nordtveit, Fernandes, Masuaku, Ayew, Calleri, Lanzini.
Subs: Randolph, Cresswell, Sakho, Fletcher, Rice, Holland, Makasi.
Everton: Stekelenburg, Holgate, Jagielka, Ashley Williams, Baines, Schneiderlin, Gana, Davies, Mirallas, Lukaku, Barkley.
Subs: Robles, Kone, Barry, Calvert-Lewin, Lookman, Pennington, Kenny.
Referee: Roger East (Wiltshire)
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WHAT THEY SAID
Slaven Bilic: "Winston Reid is back from injury. He's one of our most important players. We will see if he is going to start.
"It's a job for our defenders to stop [Romelu Lukaku]. It's not only the defenders, though. We all need to stop the service to him.
"He's not only one of the best players in the Premier League but in the whole of Europe."
Ronald Koeman: "We need a good away performance because I still think there is a little difference in the way we play, like to press and how we like to make it difficult for our opponents.
"It's all about the attitude and having that in the same way when we play at home and away. We need to start well, start aggressive and try to score. We need a little bit more of that mentality away from home.
"They have struggled a little bit and because it's a new stadium, maybe they don't feel as comfortable as they did at their old stadium. Maybe that's a reason they don't have those home performances that everyone expected."