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The Everton manager had stressed before Fulham's visit that the responsibility for finding the back of the net must not rest only on his side's strikers. “I demand more goals from my defenders and central players as well,” he declared. Idrissa Gueye and Michael Keane responded perfectly, securing a well-earned victory over the opposition's ineffective team.

Everton’s second victory in nine matches was largely untroubled as Fulham showed the reason their leading scorer this season is goals gifted by opponents. Apart from a short spell in the second half, the away side were contained all match by Everton’s superior intensity and technical ability. The Blues had three goals ruled out for infringements, but a poacher’s finish from the midfielder in first-half stoppage time and the defender's second-half header made sure there would be no reprieve for their ex-coach.

No one needed a goal more than Thierno Barry, the Everton forward who had failed to register a shot on target in 10 league games without a shot on target after his £27m summer arrival from the Spanish side and missed a gilt-edged chance to put his team 2-0 up at Sunderland on Monday. The youngster directed the first opportunity of the game over the Fulham keeper's crossbar when picked out by Iliman Ndiaye’s fine cross.

The home side controlled the early exchanges and the visiting shot-stopper pushed over the midfielder's long-range set-piece, awarded after the Fulham player was booked for hauling down Kiernan Dewsbury-Hall. Lukic brought down the same player again before halftime but the referee, the man in charge, correctly waved away Everton appeals for a second yellow. Silva was taking no further chances, though, and withdrew the player at the interval.

Barry believed his fortune had changed at last when arriving at the far post to turn in a drilled pass by Gueye. But the joy of a maiden strike was erased by an linesman's decision. The attacker was offside when going for Gueye’s cross, and failing to connect, and the video assistant referee supported the original call. Barry’s misfortune may have continued in front of goal, but his all-round performance justified the manager's choice to stick with him. His runs and effort kept busy Fulham’s central defenders 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 midfield, but the first half threat from the visitors was limited. Raúl Jiménez shot tamely at Jordon Pickford when set up in the box by his teammate and sent a set-piece from a promising location straight into the defensive barrier. That summed up their attacking output.

Everton, driven on by Dewsbury-Hall and Ndiaye, had a another strike disallowed for offside when the Fulham goalkeeper parried a Keane header and the captain volleyed in the loose ball. The home captain had moved beyond the last defender when heading on Jack Grealish’s delivery in the buildup. But the team's next effort past Leno counted. The left-back floated a perfect ball to the far post when left unmarked on the left by Tim Iroegbunam. The defender met it with a powerful nod off the crossbar and, though the midfielder fluffed his lines, his teammate the scorer converted from close range. The sense of release inside the ground was palpable.

The home side had a further effort disallowed after the restart after Dewsbury-Hall found the bottom corner from a further excellent Mykolenko cross. Ndiaye had cushioned the delivery into Barry, who was in an offside position when competing with 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 two-goal lead. Dewsbury-Hall was the creator with a corner that the defender glanced past the goalkeeper. 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 the winger. Pickford made a fine stop with his feet to deny Muniz scoring with his initial involvement and denied the speedster with another important stop in the dying moments.