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David Moyes had stressed before the match against Fulham that the responsibility for finding the back of the net should not fall solely on the team's strikers. “I want more goals from my centre-halves and midfielders as well,” he declared. Idrissa Gueye and the English defender rose to the occasion, securing a merited victory over Marco Silva’s toothless team.

The Merseyside club's second win in nine matches was largely untroubled as the visitors showed the reason their leading scorer this season is goals gifted by opponents. Aside from a short spell in the second half, the away side were kept quiet throughout by the home team's greater urgency and quality. Moyes’ team had three efforts disallowed for infringements, but a close-range strike from the midfielder in first-half stoppage time and the defender's second-half header made sure there would be no reprieve for the former Everton manager.

No one needed a goal as much as Thierno Barry, the Everton forward who had gone 10 Premier League outings without a shot on target after his big-money move 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 earliest chance of the game wide of Bernd Leno’s goal frame when found by Iliman Ndiaye’s fine cross.

Everton controlled the opening stages and the visiting shot-stopper pushed over James Garner’s long-range set-piece, given after the Fulham player was booked for fouling the Everton midfielder. The Serbian brought down the identical opponent later in the half but the official, the man in charge, rightly ignored Everton appeals for a sending off. The Fulham boss was not risking anything, however, and withdrew the player at the break.

The striker believed his fortune had finally turned when sliding in at the back post to turn in a drilled pass by Gueye. But the elation of a maiden strike was erased by an linesman's decision. The attacker was in an illegal position when attacking the delivery, and missing, and the video assistant referee backed up the original call. Barry’s misfortune may have persisted in the final third, but his all-round performance validated the manager's choice to stick with him. His movement and effort kept busy Fulham’s central defenders and helped give Everton the upper hand throughout.

The Londoners came into the contest gradually with Sander Berge and the former Everton midfielder the Nigerian working well in the engine room, but the first half threat from the away team was limited. The Mexican striker shot tamely at Jordon Pickford when teed up inside the area by Iwobi and sent a free-kick from a dangerous position straight into the Everton wall. And that was it.

Everton, inspired by Dewsbury-Hall and Ndiaye, had a second goal chalked off for an infringement when the Fulham goalkeeper saved a Keane header and James Tarkowski volleyed in the loose ball. The home captain had moved offside when heading on Jack Grealish’s cross in the build-up. But Everton’s next effort past the keeper counted. The left-back delivered a perfect ball to the far post when found in space on the left by the youngster. Tarkowski connected with a powerful nod against the bar and, though Iroegbunam fluffed his lines, his teammate Gueye finished from point-blank. The sense of release inside the ground was palpable.

Everton had a further effort ruled out early in the second half after Dewsbury-Hall found the bottom corner from another inviting Mykolenko cross. The attacker had laid off the delivery into the striker, who was in an offside position when challenging the Fulham defender for the touch that reached the home player. The team would have to wait until the 81st minute for the comfort of a two-goal lead. Dewsbury-Hall was the creator with a set-piece that the defender glanced over the goalkeeper. He did so with the upper body, and Fulham’s appeals for handball were dismissed by VAR.

Fulham posed more danger after the introductions of Josh King, the Brazilian and the winger. Pickford saved well with his legs to prevent Muniz finding the net with his first touch and stopped Traoré with a crucial save in the dying moments.