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David Moyes had stressed before Fulham's visit that the responsibility for scoring goals must not rest only on his side's forwards. “I demand more goals from my centre-halves and central players as well,” he insisted. Idrissa Gueye and the English defender duly obliged, delivering a fully deserved victory over Marco Silva’s ineffective team.

Everton’s second victory in nine matches was relatively comfortable as the visitors showed why their top marksman this season is opposition own goals. Aside from a short spell in the latter period, the visitors were kept quiet all match by Everton’s superior intensity and quality. Moyes’ team had three efforts disallowed for infringements, but a poacher’s finish from Gueye in added time before the break and Keane’s second-half header ensured 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 a shot on target after his £27m summer arrival from the Spanish side and missed a gilt-edged chance to put his team two goals ahead at the Stadium of Light on Monday. The youngster headed the first opportunity of the game wide of Bernd Leno’s goal frame when picked out by his teammate's excellent delivery.

The home side dominated the opening stages and the Fulham goalkeeper tipped over James Garner’s 30-yard free-kick, awarded after Sasa Lukic was yellow-carded for hauling down the Everton midfielder. The Serbian brought down the same player later in the half but the official, the man in charge, rightly ignored home protests for a sending off. The Fulham boss was taking no further chances, though, and substituted the midfielder at the interval.

Barry believed his fortune had changed at last when arriving at the back post to convert a low cross by Gueye. But the elation of a first Everton goal was wiped out by an linesman's decision. The attacker was offside when going for Gueye’s cross, and missing, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have persisted in the final third, but his all-round performance validated the manager's choice to keep the faith. His runs and work-rate occupied the opposition's back line and helped give the hosts the edge throughout.

The Londoners grew into the game slowly with Sander Berge and the former Everton midfielder 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 inside the area by his teammate and sent a free-kick from a dangerous position directly at the Everton wall. That summed up their attacking output.

The Blues, driven on by Dewsbury-Hall and Ndiaye, had a second goal disallowed for offside when the Fulham goalkeeper saved a effort from Keane and the captain fired home the rebound. The home captain had moved offside when nodding down the winger's cross in the build-up. But the team's next effort past Leno did stand. The left-back floated a lovely cross to the far post when left unmarked on the left by Tim Iroegbunam. The defender connected with a thumping header off the crossbar and, though the midfielder mishit the rebound, his midfield partner the scorer converted from close range. The relief inside Hill Dickinson Stadium was palpable.

Everton had a further effort ruled out after the restart after the playmaker found the bottom corner from a further excellent delivery from the left. The attacker had cushioned the ball into Barry, who was offside when competing with the Fulham defender for the ball that reached 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 set-piece that the defender glanced past the goalkeeper. He scored with the back of his shoulder, and Fulham’s appeals for handball were rejected by VAR.

Silva’s side carried more of a threat after the introductions of Josh King, Rodrigo Muniz and the winger. Pickford made a fine stop with his feet to prevent Muniz finding the net with his first touch and denied the speedster with another important stop late on.