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David Moyes had made clear before the match against Fulham that the responsibility for scoring goals must not fall solely on the team's forwards. “I demand more goals from my centre-halves and central players as well,” he stated. Idrissa Gueye and Michael Keane rose to the occasion, delivering a fully deserved victory over Marco Silva’s ineffective team.

The Merseyside club's second victory in nine outings was largely untroubled as the visitors demonstrated why their leading scorer this season is opposition own goals. Apart from a short spell in the second half, the away side were subdued throughout by Everton’s superior intensity and quality. Moyes’ team had three efforts disallowed for infringements, but a poacher’s finish from the midfielder in added time before the break and the defender's second-half header ensured there would be no reprieve for the former Everton manager.

No player needed a goal as much as Thierno Barry, the Goodison Park attacker who had failed to register a shot on target in 10 league games without testing the goalkeeper after his £27m summer arrival from Villarreal and missed a clear opportunity to put his team 2-0 up at the Stadium of Light on Monday. The youngster directed the earliest chance of the game over Bernd Leno’s goal frame when found by Iliman Ndiaye’s fine cross.

The home side controlled the opening stages and the visiting shot-stopper pushed over the midfielder's 30-yard free-kick, awarded after the Fulham player was yellow-carded for hauling down the Everton midfielder. Lukic brought down the identical opponent later in the half but the referee, Andrew Madley, correctly waved away home protests for a second yellow. The Fulham boss was taking no further chances, though, and withdrew the midfielder at the break.

Barry believed his fortune had changed at last when arriving at the back post to turn in a low cross by Gueye. But the elation of a first Everton goal was wiped out by an assistant referee’s flag. The attacker was offside when going for the delivery, and missing, and the video assistant referee supported the on-field decision. Barry’s misfortune may have continued in the final third, but his all-round performance justified Moyes’ decision to keep the faith. His movement and work-rate occupied Fulham’s central defenders and contributed to the hosts the upper hand throughout.

Fulham came into the contest gradually with Sander Berge and the former Everton midfielder the Nigerian working well in midfield, but the first half threat from the away team was limited. The Mexican striker fired weakly at the England keeper when set up inside the area by Iwobi and put a set-piece from a dangerous position straight into the defensive barrier. And that was it.

Everton, inspired by the midfielder and Ndiaye, had a second goal chalked off for an infringement when the Fulham goalkeeper saved a Keane header and the captain volleyed in the rebound. The home captain had moved offside when nodding down Jack Grealish’s delivery in the build-up. But Everton’s next effort past the keeper counted. The left-back delivered a lovely cross to the far post when found in space on the left flank by Tim Iroegbunam. Tarkowski met it with a thumping header off the crossbar and, though Iroegbunam mishit the rebound, his teammate the scorer finished from close range. The relief inside Hill Dickinson Stadium was palpable.

The home side had a third goal disallowed early in the second half after Dewsbury-Hall found the bottom corner from another inviting delivery from the left. Ndiaye had cushioned the ball into Barry, who was in an offside position when challenging the Fulham defender for the ball that reached the Everton midfielder. The team would have to wait until the closing stages for the security of a two-goal lead. Dewsbury-Hall was the architect with a corner that the defender glanced over Leno. He scored with the upper body, and the visitors' protests for handball were rejected by the video official.

Silva’s side posed more danger after the introductions of the forward, the Brazilian and Adama Traoré. The Everton keeper made a fine stop with his legs to prevent Muniz scoring with his initial involvement and stopped Traoré with another important stop in the dying moments.