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David Moyes had made clear before the match against Fulham that the responsibility for finding the back of the net must not fall solely on his side's strikers. “I expect more goals from my centre-halves and midfielders as well,” he insisted. The Senegalese midfielder and Michael Keane rose to the occasion, securing a merited victory over the opposition's toothless team.

The Merseyside club's second victory in nine matches was largely untroubled as the visitors showed the reason their top marksman this season is opposition own goals. Apart from a short spell in the second half, the away side were kept quiet throughout by the home team's superior intensity and quality. Moyes’ team had three goals ruled out for offside, but a poacher’s finish from Gueye in added time before the break and Keane’s late conversion ensured there would be no reprieve for their ex-coach.

No player was more in need of scoring as much as the young striker, the Everton forward 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 the Stadium of Light earlier in the week. The 23-year-old headed the first opportunity of the game over Bernd Leno’s crossbar when found by Iliman Ndiaye’s excellent delivery.

The home side controlled the early exchanges and the Fulham goalkeeper pushed over the midfielder's long-range set-piece, awarded after the Fulham player was yellow-carded for fouling the Everton midfielder. Lukic brought down the identical opponent again before halftime but the official, Andrew Madley, correctly waved away home protests for a second yellow. Silva was not risking anything, though, and withdrew the player at the interval.

The striker thought his luck had changed at last when arriving at the far post to convert a drilled pass by his teammate. But the joy of a maiden strike was erased by an assistant referee’s flag. The attacker was in an illegal position when attacking Gueye’s cross, and missing, and the VAR backed up the original call. Barry’s misfortune may have continued in front of goal, but his all-round performance 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 gradually with Sander Berge and the ex-Goodison player the Nigerian working well in midfield, but the first half threat from the away team was limited. The Mexican striker fired weakly at Jordon Pickford when set up in the box by his teammate and put a free-kick from a promising location directly at the Everton wall. That summed up their attacking output.

Everton, inspired by the midfielder and Ndiaye, had a second goal disallowed for an infringement when the Fulham goalkeeper parried a Keane header and James Tarkowski volleyed in the rebound. The home captain had just strayed offside when heading on Jack Grealish’s cross in the build-up. But the team's third attempt past the keeper did stand. Vitalii Mykolenko floated a lovely cross to the far post when found in space on the left flank by Tim Iroegbunam. The defender met it with a powerful nod against the bar and, though the midfielder mishit the rebound, his midfield partner Gueye converted from point-blank. The relief inside Hill Dickinson Stadium was palpable.

The home side had a third goal disallowed after the restart after the playmaker found the bottom corner from another inviting Mykolenko cross. The attacker had cushioned the ball into Barry, who was offside when challenging the Fulham defender for the touch that fell to the home player. Everton would have to wait until the 81st minute for the security of a second goal. Dewsbury-Hall was the creator with a corner that Keane directed past the goalkeeper. He did so with the upper body, and Fulham’s appeals for handball were dismissed by VAR.

Fulham carried more of a threat following the substitutions of Josh King, Rodrigo Muniz and the winger. The Everton keeper saved well with his legs to prevent Muniz scoring with his first touch and denied Traoré with a crucial save in the dying moments.