A defeat for West Ham would have seen it lose its opening five league games of a season for the first time, but it showed plenty of craft in attack to punish Everton's sloppy defending.

Although Marco Silva's men initially looked the brighter, they were completely caught out for Yarmolenko's opener in the 11th minute, before the Ukrainian – starting his first Premier League game – added a stunning second just after the half-hour mark.

Gylfi Sigurdsson pulled one back just before the interval, but West Ham ultimately killed off Everton’s chances in the 61st minute through Arnautovic's well-worked goal, ending its woeful run of form.

Pellegrini's decision to name a three-pronged attack showed West Ham's intent and two of them combined for the opener – Arnautovic racing in behind Everton's defence and squaring to Yarmolenko for an easy finish.

Yarmolenko then stunned Everton with a second 20 minutes later, running at Kurt Zouma before cutting on to his left foot to bend a sumptuous effort beyond Jordan Pickford from 18 yards out.

Everton was handed a lifeline just before the break, Sigurdsson powering a header past Lukasz Fabianski from Jonjoe Kenny's cross.

Everton was buoyed by that goal and piled the pressure on after the restart, only for West Ham to restore its two-goal cushion past the hour – Arnautovic prodding home following a neat interchange with Pedro Obiang.

The host poured men forward desperately towards the end, with substitute Oumar Niasse turning Lucas Digne's cross against the woodwork, but West Ham held firm to claim a deserved win.