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David Moyes had made clear before the match against Fulham that the onus for finding the back of the net must not rest only on the team's strikers. “I expect more goals from my centre-halves and midfielders as well,” he declared. The Senegalese midfielder and Michael Keane duly obliged, delivering a merited victory over Marco Silva’s ineffective side.

Everton’s second win in nine outings was relatively comfortable as the visitors showed why their top marksman this season is goals gifted by opponents. Apart from a brief flurry in the latter period, the visitors were contained throughout by Everton’s greater urgency and technical ability. Moyes’ team had three goals disallowed for offside, but a poacher’s finish from Gueye in first-half stoppage time and Keane’s second-half header made sure there would be no reprieve for their ex-coach.

No player was more in need of scoring more than the young striker, the Everton forward who had gone 10 Premier League outings without a shot on target after his £27m summer arrival from the Spanish side and spurned a clear opportunity to put his team 2-0 up at the Stadium of Light earlier in the week. The 23-year-old directed the first opportunity of the game wide of Bernd Leno’s goal frame when found by Iliman Ndiaye’s excellent delivery.

Everton dominated the early exchanges and the Fulham goalkeeper tipped over James Garner’s long-range set-piece, awarded after the Fulham player was booked for hauling down Kiernan Dewsbury-Hall. Lukic brought down the identical opponent again before halftime but the official, the man in charge, correctly waved away home protests for a sending off. Silva was taking no further chances, however, and withdrew the midfielder at the break.

The striker believed his fortune had changed at last when sliding in at the far post to turn in a low cross by his teammate. But the elation of a maiden strike was wiped out by an assistant referee’s flag. Ndiaye was in an illegal position when going for the delivery, and missing, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have continued in front of goal, but his all-round performance justified Moyes’ decision to stick with him. His movement and work-rate occupied Fulham’s central defenders and contributed to Everton the upper hand throughout.

The Londoners came into the contest gradually with the Norwegian and the ex-Goodison player the Nigerian combining effectively in midfield, but the early danger from the visitors was limited. The Mexican striker fired weakly at the England keeper when set up inside the area by Iwobi and sent a set-piece from a dangerous position directly at the Everton wall. And that was it.

The Blues, inspired by Dewsbury-Hall and Ndiaye, had a another strike chalked off for offside when Leno parried a Keane header and James Tarkowski fired home the rebound. The skipper had just strayed beyond the last defender when nodding down Jack Grealish’s delivery in the buildup. But the team's third attempt past the keeper counted. The left-back floated a lovely cross to the back post when found in space on the left flank by Tim Iroegbunam. The defender met it with a thumping header off the crossbar and, though the midfielder mishit the rebound, his teammate Gueye finished from point-blank. The relief inside Hill Dickinson Stadium was palpable.

Everton had a further effort disallowed after the restart after the playmaker found the bottom corner from a further excellent Mykolenko cross. The attacker had cushioned the ball into the striker, who was in an offside position when challenging Joachim Anderson for the ball that reached the Everton midfielder. The team would have to be patient until the 81st minute for the security of a two-goal lead. The provider was the creator with a corner that the defender directed past the goalkeeper. He did so with the back of his shoulder, and the visitors' protests for handball were dismissed by the video official.

Fulham carried more of a threat after the introductions of the forward, the Brazilian and the winger. Pickford saved well with his feet to deny the substitute scoring with his first touch and denied Traoré with another important stop in the dying moments.