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David Moyes had emphasized before the match against Fulham that the onus for scoring goals must not fall solely on his side's forwards. “I demand 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 team.

Everton’s second win in nine matches was relatively comfortable as the visitors highlighted why their top marksman this season is goals gifted by opponents. Aside from a brief flurry in the latter period, the away side were subdued throughout by the home team's greater urgency and quality. Moyes’ team had three goals disallowed for offside, but a close-range strike from the midfielder in first-half stoppage time and Keane’s second-half header made sure there would be no reprieve for their ex-coach.

No player 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 Villarreal and spurned a gilt-edged chance to put his team two goals ahead at Sunderland on Monday. The 23-year-old headed the first opportunity of the game wide of Bernd Leno’s goal frame when picked out by Iliman Ndiaye’s excellent delivery.

The home side dominated the opening stages and the Fulham goalkeeper tipped over James Garner’s 30-yard free-kick, awarded after Sasa Lukic was booked for fouling the Everton midfielder. Lukic brought down the same player later in the half but the official, Andrew Madley, correctly waved away Everton appeals for a second yellow. The Fulham boss was not risking anything, though, and withdrew the midfielder at the interval.

The striker believed his fortune had finally turned when sliding in at the far post to turn in a low cross by his teammate. But the elation of a first Everton goal was wiped out by an linesman's decision. Ndiaye was offside when attacking the delivery, and missing, and the video assistant referee supported the original call. Barry’s misfortune may have persisted in the final third, but his all-round performance justified Moyes’ decision to keep the faith. His runs and work-rate occupied the opposition's back line and helped give Everton the edge throughout.

Fulham came into the contest gradually with Sander Berge and the ex-Goodison player Alex Iwobi combining effectively in midfield, but the first half threat from the away team was minimal. Raúl Jiménez shot tamely 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 Everton wall. And that was it.

The Blues, inspired by Dewsbury-Hall and the forward, had a second goal disallowed for offside when Leno parried a effort from Keane and the captain fired home the rebound. The home captain had moved beyond the last defender when heading on Jack Grealish’s cross in the build-up. But the team's third attempt past Leno did stand. The left-back delivered a perfect ball to the back post when found in space on the left by the youngster. The defender connected with a thumping header against the bar and, though the midfielder mishit the rebound, his teammate the scorer converted from point-blank. The relief inside Hill Dickinson Stadium was evident.

Everton had a third goal ruled out early in the second half after the playmaker scored from another inviting Mykolenko cross. Ndiaye had laid off the ball into the striker, who was in an offside position when challenging Joachim Anderson for the touch that fell to the home player. The team would have to be patient until the closing stages for the security of a two-goal lead. Dewsbury-Hall was the creator with a set-piece that the defender directed past the goalkeeper. He scored with the upper body, and the visitors' protests for handball were dismissed by VAR.

Silva’s side carried more of a threat after the substitutions of the forward, the Brazilian and Adama Traoré. The Everton keeper saved well with his legs to deny the substitute scoring with his initial involvement and denied the speedster with another important stop in the dying moments.