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David Moyes had stressed before Fulham's visit that the onus for scoring goals should not rest only on his side's strikers. “I want more goals from my centre-halves and central players as well,” he declared. Idrissa Gueye and the English defender duly obliged, securing a merited victory over Marco Silva’s toothless side.

The Merseyside club's second win in nine outings was relatively comfortable as Fulham showed why their leading scorer 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 technical ability. Moyes’ team had three efforts ruled out for offside, 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 reprieve for their ex-coach.

No one 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 big-money move from the Spanish side and spurned a clear opportunity to put his team 2-0 up at Sunderland on Monday. The youngster directed the first opportunity of the game wide of the Fulham keeper's crossbar when found by Iliman Ndiaye’s fine cross.

The home side controlled the opening stages and the Fulham goalkeeper tipped over the midfielder's long-range set-piece, given after Sasa Lukic was booked for fouling the Everton midfielder. Lukic brought down the identical opponent later in the half but the official, the man in charge, correctly waved away home protests for a sending off. The Fulham boss was not risking anything, though, and withdrew the player at the break.

Barry believed his luck had changed at last when sliding in at the far post to turn in a drilled pass by Gueye. But the elation of a first Everton goal was erased by an linesman's decision. The attacker was offside when attacking Gueye’s cross, and missing, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have continued in the final third, but his overall display validated Moyes’ decision to keep the faith. His movement and work-rate occupied the opposition's back line and contributed to the hosts the upper hand all game.

The Londoners came into the contest slowly with Sander Berge and the former Everton midfielder the Nigerian combining effectively in the engine room, but the first half threat from the visitors was minimal. Raúl Jiménez fired weakly at the England keeper when set up inside the area by his teammate and put a set-piece from a promising location directly at the defensive barrier. That summed up their attacking output.

The Blues, inspired by the midfielder and the forward, had a second goal disallowed for an infringement when the Fulham goalkeeper saved a effort from Keane and the captain fired home the rebound. The home captain had just strayed beyond the last defender when nodding down the winger's cross in the buildup. But the team's third attempt beating the keeper did stand. Vitalii Mykolenko floated a lovely cross to the back post when left unmarked on the left flank by Tim Iroegbunam. Tarkowski connected with a thumping header against the bar and, though the midfielder mishit the rebound, his teammate Gueye finished from close range. The sense of release inside Hill Dickinson Stadium was evident.

Everton had a further effort ruled out early in the second half after the playmaker found the bottom corner from a further excellent Mykolenko cross. Ndiaye had cushioned the ball into Barry, who was offside when competing with the Fulham defender for the ball that fell to the home player. The team would have to be patient until the 81st minute for the comfort of a second goal. Dewsbury-Hall was the architect with a set-piece that the defender glanced past the goalkeeper. He scored with the upper body, and the visitors' protests for handball were rejected by VAR.

Fulham posed more danger following the introductions of Josh King, Rodrigo Muniz and the winger. Pickford made a fine stop with his legs to deny the substitute finding the net with his first touch and stopped the speedster with a crucial save in the dying moments.