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The Everton manager had emphasized before Fulham's visit that the onus for scoring goals should not fall solely on his side's forwards. “I want more goals from my centre-halves and midfielders as well,” he declared. Idrissa Gueye and the English defender rose to the occasion, earning a merited victory over Marco Silva’s toothless team.

Everton’s second win in nine matches was relatively comfortable as Fulham highlighted why their leading scorer this season is goals gifted by opponents. Apart from a short spell in the latter period, the away side were subdued all match by the home team's greater urgency and quality. Moyes’ team had three goals ruled out for infringements, but a close-range strike from the midfielder in added time before the break and Keane’s late conversion ensured there would be no comeback for their ex-coach.

No one needed a goal as much as the young striker, the Everton attacker who had gone 10 Premier League outings without testing the goalkeeper after his £27m summer arrival from the Spanish side and missed a clear opportunity to put his team 2-0 up at Sunderland on Monday. The 23-year-old directed the first opportunity of the game over Bernd Leno’s goal frame when picked out by Iliman Ndiaye’s fine cross.

The home side dominated the early exchanges and the Fulham goalkeeper tipped over James Garner’s long-range set-piece, awarded after Sasa Lukic was booked for fouling the Everton midfielder. The Serbian tripped the same player later in the half but the referee, the man in charge, correctly waved away home protests for a sending off. Silva was taking no further chances, though, and substituted the player at the break.

Barry believed his fortune had changed at last when sliding in at the far post to convert a low cross by his teammate. But the elation of a maiden strike was wiped out by an linesman's decision. The attacker was offside when going for Gueye’s cross, and failing to connect, and the VAR backed up the on-field decision. The forward's bad luck may have continued in the final third, but his overall display justified the manager's choice to keep the faith. His runs and effort kept busy Fulham’s central defenders and helped give Everton the edge all game.

The Londoners came into the contest slowly with Sander Berge and the former Everton midfielder Alex Iwobi working well in the engine room, but the first half threat from the away team was minimal. Raúl Jiménez fired weakly at Jordon Pickford when teed up inside the area by his teammate and put a free-kick from a promising location straight into the defensive barrier. And that was it.

Everton, driven on by Dewsbury-Hall and the forward, had a second goal chalked off for an infringement when Leno saved a effort from Keane and James Tarkowski fired home the loose ball. The skipper had just strayed beyond the last defender when nodding down Jack Grealish’s cross in the buildup. But the team's next effort beating Leno counted. Vitalii Mykolenko delivered a perfect ball to the back post when found in space on the left by the youngster. Tarkowski met it with a powerful nod against the bar and, though the midfielder mishit the rebound, his midfield partner the scorer converted from close range. The relief inside Hill Dickinson Stadium was evident.

Everton had a further effort ruled out after the restart after Dewsbury-Hall scored from a further excellent Mykolenko cross. Ndiaye had cushioned the ball into the striker, who was in an offside position when competing with the Fulham defender for the touch that reached the Everton midfielder. Everton would have to be patient until the 81st minute for the comfort of a second goal. Dewsbury-Hall was the creator with a set-piece that the defender directed over Leno. He did so with the back of his shoulder, and Fulham’s appeals for handball were rejected by VAR.

Fulham carried more of a threat following the substitutions of Josh King, the Brazilian and the winger. The Everton keeper made a fine stop with his legs to prevent the substitute finding the net with his first touch and denied Traoré with another important stop late on.