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David Moyes had made clear before Fulham's visit that the responsibility for finding the back of the net should not rest only on his side's forwards. “I demand more goals from my defenders and midfielders as well,” he insisted. The Senegalese midfielder and Michael Keane responded perfectly, securing a well-earned victory over Marco Silva’s ineffective side.

Everton’s second win in nine matches was fairly straightforward as Fulham demonstrated why their top marksman this season is goals gifted by opponents. Aside from a short spell in the second half, the away side were subdued throughout by Everton’s superior intensity and technical ability. Moyes’ team had three goals ruled out for offside, but a close-range strike from Gueye in added time before the break and Keane’s late conversion made sure there would be no reprieve for their ex-coach.

No one needed a goal as much as the young striker, the Goodison Park attacker who had gone 10 Premier League outings without a shot on target after his £27m summer arrival from the Spanish side and missed a gilt-edged chance to put his team 2-0 up at Sunderland on Monday. The 23-year-old directed the earliest chance of the game wide of the Fulham keeper's crossbar when found by Iliman Ndiaye’s fine cross.

The home side dominated the early exchanges and the Fulham goalkeeper tipped over James Garner’s long-range set-piece, given after Sasa Lukic was booked for fouling Kiernan Dewsbury-Hall. The Serbian tripped the same player later in the half but the referee, Andrew Madley, correctly waved away home protests for a second yellow. Silva was not risking anything, though, and substituted the player at the interval.

The striker believed his fortune had finally turned 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 offside when attacking Gueye’s cross, and failing to connect, and the VAR backed up the on-field decision. Barry’s misfortune may have persisted in the final third, but his overall display validated the manager's choice to stick with him. His runs and work-rate kept busy Fulham’s central defenders and helped give Everton the edge 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 limited. The Mexican striker shot tamely at Jordon Pickford when teed up in the box by his teammate and sent a set-piece from a promising location straight into the defensive barrier. That summed up their attacking output.

Everton, inspired by Dewsbury-Hall and Ndiaye, had a another strike disallowed for offside when the Fulham goalkeeper saved a effort from Keane and James Tarkowski volleyed in the loose ball. The home captain had just strayed beyond the last defender when heading on Jack Grealish’s delivery in the build-up. But the team's third attempt past Leno did stand. Vitalii Mykolenko delivered a perfect ball to the far post when found in space on the left by Tim Iroegbunam. Tarkowski met it with a powerful nod against the bar and, though Iroegbunam mishit the rebound, his teammate the scorer finished from point-blank. The sense of release inside Hill Dickinson Stadium was evident.

Everton had a further effort ruled out after the restart after Dewsbury-Hall scored from another inviting Mykolenko cross. The attacker had cushioned the delivery into Barry, who was in an offside position when competing with the Fulham defender for the ball that fell to the Everton midfielder. The team would have to be patient until the closing stages for the security of a second goal. The provider was the architect with a corner that Keane directed past Leno. He scored with the back of his shoulder, and Fulham’s appeals for handball were rejected by the video official.

Silva’s side posed more danger following the substitutions of Josh King, Rodrigo Muniz and the winger. The Everton keeper made a fine stop with his feet to prevent the substitute finding the net with his first touch and denied the speedster with a crucial save late on.