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David Moyes had stressed before Fulham's visit that the responsibility for scoring goals must not rest only on his side's forwards. “I demand more goals from my centre-halves and central players as well,” he insisted. Idrissa Gueye and the English defender rose to the occasion, earning a fully deserved victory over Marco Silva’s toothless team.

Everton’s second win in nine outings was largely untroubled as Fulham demonstrated why their top marksman this season is goals gifted by opponents. Apart from a short spell in the second half, the visitors were subdued all match by Everton’s greater urgency and technical ability. Moyes’ team had three efforts ruled out for offside, but a poacher’s finish from Gueye in added time before the break and the defender's late conversion ensured there would be no reprieve for their ex-coach.

No player needed a goal more than Thierno Barry, the Everton attacker who had gone 10 Premier League outings without a shot on target after his £27m summer arrival from Villarreal and missed a gilt-edged chance to put his team 2-0 up at Sunderland earlier in the week. The 23-year-old headed the earliest chance of the game wide of Bernd Leno’s crossbar when picked out by his teammate's excellent delivery.

The home side dominated the opening stages and the Fulham goalkeeper tipped over the midfielder's 30-yard free-kick, awarded after the Fulham player was yellow-carded for hauling down Kiernan Dewsbury-Hall. The Serbian tripped the identical opponent again before halftime but the referee, Andrew Madley, rightly ignored Everton appeals for a sending off. Silva was not risking anything, though, and withdrew the midfielder at the break.

Barry believed his fortune had changed at last when sliding in at the far post to convert a drilled pass by Gueye. But the joy of a maiden strike was erased by an linesman's decision. The attacker was in an illegal position when attacking Gueye’s cross, and failing to connect, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have continued in front of goal, but his overall display validated the manager's choice to keep the faith. His runs and effort kept busy the opposition's back line and contributed to the hosts the edge throughout.

The Londoners came into the contest slowly with the Norwegian and the ex-Goodison player the Nigerian combining effectively in midfield, but the early danger from the away team was minimal. Raúl Jiménez fired weakly at Jordon Pickford when set up inside the area by Iwobi and put a set-piece from a dangerous position straight into the Everton wall. That summed up their attacking output.

Everton, inspired by the midfielder and Ndiaye, had a second goal chalked off for offside when the Fulham goalkeeper saved a Keane header and the captain fired home the rebound. The skipper had just strayed beyond the last defender when heading on Jack Grealish’s delivery in the buildup. But the team's next effort beating Leno did stand. The left-back floated a lovely cross to the back post when left unmarked on the left flank by the youngster. Tarkowski connected with a powerful nod against the bar and, though the midfielder mishit the rebound, his teammate the scorer converted from point-blank. The relief inside Hill Dickinson Stadium was palpable.

The home side had a further effort disallowed early in the second half after Dewsbury-Hall found the bottom corner from a further excellent Mykolenko cross. Ndiaye had cushioned the delivery into Barry, who was offside when competing with Joachim Anderson for the touch that fell to the home player. The team would have to be patient until the closing stages for the security of a two-goal lead. Dewsbury-Hall was the creator with a set-piece that Keane glanced past the goalkeeper. He did so with the upper body, and Fulham’s appeals for handball were rejected by the video official.

Silva’s side posed more danger following the introductions of the forward, the Brazilian and the winger. The Everton keeper made a fine stop with his legs to prevent Muniz scoring with his first touch and stopped the speedster with a crucial save late on.