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David Moyes had stressed before Fulham's visit that the responsibility for scoring goals must not fall solely on the team's strikers. “I expect more goals from my centre-halves and midfielders as well,” he stated. The Senegalese midfielder and the English defender duly obliged, securing a merited victory over Marco Silva’s toothless side.

The Merseyside club's second win in nine outings was relatively comfortable as the visitors highlighted the reason their top marksman this season is goals gifted by opponents. Apart from a brief flurry in the second half, the away side were subdued all match by the home team's greater urgency and technical ability. The Blues had three goals ruled out for offside, but a poacher’s finish from the midfielder in added time before the break and the defender's late conversion made sure there would be no reprieve for the former Everton manager.

No player needed a goal more than the young striker, the Goodison Park forward who had failed to register a shot on target in 10 league games 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 on Monday. The youngster headed the first opportunity of the game wide of Bernd Leno’s goal frame when picked out by Iliman Ndiaye’s fine cross.

Everton dominated the opening stages and the visiting shot-stopper tipped over James Garner’s 30-yard free-kick, awarded after the Fulham player was booked for fouling the Everton midfielder. The Serbian tripped the same player later in the half but the official, Andrew Madley, rightly ignored home protests for a sending off. The Fulham boss was taking no further chances, however, and substituted the midfielder at the interval.

Barry thought his luck had changed at last when sliding in at the far post to turn in a drilled pass by his teammate. 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 missing, and the video assistant referee supported the original call. Barry’s misfortune may have continued in front of goal, but his overall display validated the manager's choice to stick with him. His runs and effort kept busy Fulham’s central defenders and helped give Everton the upper hand all game.

Fulham grew into the game slowly with the Norwegian and the ex-Goodison player Alex Iwobi working well in the engine room, but the early danger from the visitors was minimal. Raúl Jiménez shot tamely at the England keeper when teed up in the box by Iwobi and put a set-piece from a dangerous position directly at the defensive barrier. That summed up their attacking output.

Everton, inspired by the midfielder and the forward, had a another strike disallowed for offside when Leno saved a Keane header and the captain volleyed in the loose ball. The skipper had just strayed offside when nodding down Jack Grealish’s delivery in the build-up. But Everton’s third attempt beating the keeper counted. Vitalii Mykolenko delivered a perfect ball to the far post when found in space on the left flank by Tim Iroegbunam. The defender connected with a powerful nod off the crossbar and, though Iroegbunam mishit the rebound, his midfield partner Gueye finished from point-blank. The relief inside the ground was palpable.

Everton had a third goal disallowed early in the second half after the playmaker scored from a further excellent delivery from the left. Ndiaye had cushioned the delivery into the striker, who was in an offside position when competing with Joachim Anderson for the ball that fell to the home player. Everton would have to be patient until the closing stages for the comfort of a two-goal lead. Dewsbury-Hall was the architect with a corner that the defender directed past Leno. He scored with the upper body, and the visitors' protests for handball were rejected by VAR.

Fulham posed more danger following the substitutions of Josh King, Rodrigo Muniz and the winger. Pickford saved well with his feet to prevent Muniz finding the net with his initial involvement and denied the speedster with a crucial save late on.