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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 the team's strikers. “I want more goals from my centre-halves and midfielders as well,” he declared. Idrissa Gueye and Michael Keane responded perfectly, securing a well-earned victory over the opposition's toothless side.

Everton’s second win in nine matches was relatively comfortable as the visitors highlighted the reason their leading scorer this season is opposition own goals. Aside from a short spell in the second half, the visitors were contained throughout by the home team's greater urgency and technical ability. The Blues had three goals disallowed for infringements, but a poacher’s finish from Gueye in first-half stoppage time and the defender's second-half header made sure there would be no comeback for the former Everton manager.

No one needed a goal as much as Thierno Barry, the Goodison Park attacker who had gone 10 Premier League outings without a shot on target after his £27m summer arrival from Villarreal and spurned a gilt-edged chance to put his team 2-0 up at Sunderland on Monday. The youngster headed the earliest chance 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 visiting shot-stopper tipped over the midfielder's 30-yard free-kick, given after the Fulham player was booked for hauling down Kiernan Dewsbury-Hall. The Serbian tripped the same player later in the half but the referee, Andrew Madley, rightly ignored Everton appeals for a second yellow. The Fulham boss was taking no further chances, though, and withdrew the midfielder at the break.

The striker believed his luck had finally turned when sliding in at the back post to convert a low cross by his teammate. But the elation of a maiden strike was erased by an linesman's decision. The attacker was in an illegal position when attacking Gueye’s cross, and failing to connect, and the video assistant referee supported 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 runs and effort kept busy the opposition's back line and contributed to Everton the upper hand all game.

Fulham came into the contest gradually with Sander Berge and the former Everton midfielder the Nigerian combining effectively in the engine room, but the early danger from the visitors was limited. The Mexican striker shot tamely at Jordon Pickford when set up inside the area by Iwobi and put 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 an infringement when the Fulham goalkeeper saved a effort from Keane and James Tarkowski volleyed in the loose ball. The skipper had moved beyond the last defender when nodding down the winger's cross in the buildup. But Everton’s third attempt past the keeper did stand. The left-back floated a perfect ball to the far post when found in space on the left flank by Tim Iroegbunam. The defender met it with a powerful nod off the crossbar and, though Iroegbunam fluffed his lines, his teammate Gueye finished from point-blank. The relief inside the ground was palpable.

Everton had a further effort disallowed after the restart after Dewsbury-Hall scored from a further excellent Mykolenko cross. Ndiaye had cushioned the delivery into the striker, who was offside when challenging the Fulham defender for the touch that reached the Everton midfielder. Everton would have to wait until the closing stages for the comfort of a second goal. The provider was the architect with a set-piece that Keane glanced over Leno. He did so with the back of his shoulder, and Fulham’s appeals for a handball were rejected by VAR.

Fulham carried more of a threat after the substitutions of the forward, Rodrigo Muniz and Adama Traoré. Pickford saved well with his legs to prevent the substitute finding the net with his first touch and denied the speedster with a crucial save late on.