In what was the last top-flight game before the international break, Neal Maupay scored his first Everton goal with a fine finish after the break to give the Toffees a much-needed three points, lifting them to 13th in the table.
As for the Hammers, defeat continued what has been an incredibly poor start to the campaign domestically, with David Moyes’ side still far short of the standards they have set in recent seasons.
They will have to spend the next two weeks watching themselves in the relegation zone, with just four points and three goals scored in their first seven league games.
Everton were again without Dominic Calvert-Lewin, despite suggestions he could return from injury, while Michail Antonio was given the nod for the visitors, despite Gianluca Scamacca being put on the scoresheet in Europe mid-week.
Both teams came into the game with eight points and seven goals combined in their first six Premier League games, so the odds were limited in the opening 45 minutes was no surprise.
Antonio briefly thought he was ready for a tap-in at the back post, only for Conor Coady to somehow deflect him while avoiding his own net, and the Hammers racked up eight corners in the first half time.
None were particularly dangerous, however, and it was Everton who were the better team overall, with Amadou Onana, who the Hammers were close to signing in the summer, a real threat in the air. There was a lot of intensity and heavy challenges, with fans having to settle for those in the absence of any real quality.
There were chances at both ends immediately after the break, with Jarrod Bowen shooting over the bar and Demarai Gray then curling an effort straight at Lukasz Fabianski. The opportunities were finally presenting themselves and it wasn’t long before one was taken.
Maupay couldn’t come out on top for Everton in the Merseyside derby on his debut, but he did it this time, and in brilliant fashion. He spun around the edge of the box before firing quickly, firing past Fabianski at his nearest post.
It was almost tenth lucky for West Ham from corners, as they pushed to equalize. Tomas Soucek crossed his man at the near post but his graze header bounced just wide of the far post. Said Benrahma, featured off the bench as Maxwel Cornet and Scamacca also came on, came as close as anyone to leveling things as he saw his curling effort hit inside the post.
Alex Iwobi had a decent chance to double the lead but couldn’t reduce his effort, although it was a rare foray into West Ham territory for Everton once they took the lead with lockdown being the name of the game rather than ambition. The hosts’ time-wasting tactics frustrated Moyes as he raced down the field to act as a very experienced ball boy in the closing stages, trying in vain to get an Everton free kick early.
Cornet had a few chances to equalise, the first parried by Asmir Begovic and the second fired into the side netting as he was forced wider and wider around the goalkeeper.
A 14th corner from West Ham caused an all-powerful scramble in stoppage time, Declan Rice headed the ball towards goal, but a team-mate was unable to provide the finishing touch. After a big summer transfer window, the Hammers have made their worst start to the Premier League season.