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David Moyes had stressed before Fulham's visit that the responsibility for finding the back of the net must not rest only on the team's strikers. “I expect more goals from my centre-halves and midfielders as well,” he declared. Idrissa Gueye and the English defender responded perfectly, securing a merited victory over Marco Silva’s toothless side.

The Merseyside club's second victory in nine matches was fairly straightforward as the visitors highlighted why their leading scorer this season is goals gifted by opponents. Aside from a brief flurry in the latter period, the visitors were subdued all match by Everton’s superior intensity and quality. Moyes’ team had three goals disallowed for infringements, but a close-range strike from Gueye in added time before the break and the defender's late conversion ensured there would be no comeback for their ex-coach.

No one needed a goal as much as Thierno Barry, the Goodison Park forward 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 the Stadium of Light on Monday. The youngster directed the first opportunity of the game wide of the Fulham keeper's crossbar when found by his teammate's excellent delivery.

Everton dominated the early exchanges and the Fulham goalkeeper pushed over James Garner’s 30-yard free-kick, awarded after the Fulham player was booked for fouling the Everton midfielder. Lukic brought down the same player later in the half but the referee, Andrew Madley, correctly waved away home protests for a sending off. Silva was taking no further chances, however, and withdrew the player at the interval.

Barry believed his luck had finally turned when arriving at the far post to convert a drilled pass by Gueye. But the elation of a first Everton goal was wiped out by an assistant referee’s flag. The attacker was offside when attacking Gueye’s cross, and failing to connect, and the VAR backed up the on-field decision. Barry’s misfortune may have persisted in front of goal, but his overall display justified the manager's choice to stick with him. His runs and work-rate kept busy the opposition's back line and contributed to Everton the edge all game.

The Londoners grew into the game gradually with Sander Berge and the former Everton midfielder Alex Iwobi combining effectively in midfield, but the early danger from the visitors was minimal. The Mexican striker fired weakly at Jordon Pickford when teed up inside the area by his teammate and put a set-piece from a dangerous position directly at the defensive barrier. That summed up their attacking output.

The Blues, inspired by the midfielder and Ndiaye, had a another strike disallowed for offside when Leno parried a Keane header and James Tarkowski fired home the rebound. The home captain had just strayed offside when heading on Jack Grealish’s delivery in the build-up. But the team's next effort past Leno did stand. Vitalii Mykolenko floated a perfect ball to the back post when left unmarked on the left flank by the youngster. Tarkowski connected with a thumping header against the bar and, though the midfielder mishit the rebound, his teammate the scorer converted from close range. The relief inside Hill Dickinson Stadium was palpable.

The home side had a further effort ruled out after the restart after Dewsbury-Hall found the bottom corner from another inviting delivery from the left. Ndiaye had laid off the ball into the striker, who was in an offside position when competing with 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 second goal. Dewsbury-Hall was the creator with a corner that Keane directed over Leno. He did so with the back of his shoulder, and the visitors' protests for handball were dismissed by the video official.

Silva’s side carried more of a threat after the introductions of Josh King, the Brazilian and the winger. Pickford made a fine stop with his legs to prevent Muniz scoring with his first touch and denied the speedster with a crucial save late on.