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David Moyes had made clear before the match against Fulham that the responsibility for scoring goals should not fall solely on his side's strikers. “I demand more goals from my defenders and central players as well,” he declared. The Senegalese midfielder and the English defender responded perfectly, securing a well-earned victory over Marco Silva’s toothless team.

The Merseyside club's second win in nine outings was relatively comfortable as the visitors demonstrated the reason their leading scorer this season is opposition own goals. Aside from a short spell in the second half, the away side were kept quiet throughout by the home team's greater urgency and technical ability. Moyes’ team had three goals disallowed for infringements, but a poacher’s finish from Gueye in added time before the break and the defender's second-half header made sure there would be no comeback for the former Everton manager.

No one was more in need of scoring more than the young striker, the Everton forward who had gone 10 Premier League outings without testing the goalkeeper after his £27m summer arrival from the Spanish side and missed a gilt-edged chance to put his team 2-0 up at Sunderland earlier in the week. The 23-year-old directed the first opportunity of the game over the Fulham keeper's goal frame when found by Iliman Ndiaye’s excellent delivery.

The home side dominated the early exchanges and the Fulham goalkeeper pushed over James Garner’s 30-yard free-kick, awarded after Sasa Lukic was booked for fouling the Everton midfielder. The Serbian brought down the same player again before halftime but the referee, Andrew Madley, correctly waved away Everton appeals for a second yellow. The Fulham boss was not risking anything, though, and withdrew the player at the interval.

The striker believed his luck had changed at last when arriving at the back post to convert a drilled pass by Gueye. But the joy of a first Everton goal was erased by an assistant referee’s flag. Ndiaye was offside when attacking the delivery, and failing to connect, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have persisted in the final third, but his overall display validated Moyes’ decision to keep the faith. His movement and effort kept busy Fulham’s central defenders and contributed to the hosts the upper hand throughout.

The Londoners came into the contest gradually with the Norwegian and the former Everton midfielder Alex Iwobi working well in the engine room, but the early danger from the visitors was limited. Raúl Jiménez fired weakly at Jordon Pickford when set up in the box by Iwobi and put a free-kick from a dangerous position straight into the defensive barrier. And that was it.

Everton, driven on by Dewsbury-Hall and the forward, had a second goal disallowed for an infringement when the Fulham goalkeeper saved a Keane header and the captain fired home the rebound. The home captain had just strayed offside when heading on Jack Grealish’s delivery in the buildup. But Everton’s third attempt past the keeper counted. Vitalii Mykolenko delivered a perfect ball to the far post when left unmarked on the left flank by Tim Iroegbunam. The defender met it with a thumping header off the crossbar and, though Iroegbunam mishit the rebound, his midfield partner Gueye finished from point-blank. The sense of release inside Hill Dickinson Stadium was evident.

Everton had a third goal disallowed after the restart after the playmaker scored from a further excellent delivery from the left. The attacker had laid off the ball into Barry, who was offside when challenging the Fulham defender for the touch that reached the home player. The team would have to be patient until the 81st minute for the comfort of a second goal. The provider was the architect with a set-piece that Keane glanced past the goalkeeper. He scored with the upper body, and the visitors' protests for handball were dismissed by the video official.

Fulham posed more danger following the substitutions of the forward, the Brazilian and the winger. Pickford saved well with his feet to prevent Muniz finding the net with his initial involvement and stopped Traoré with a crucial save in the dying moments.