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David Moyes had made clear before the match against Fulham that the responsibility for scoring goals must not rest only on the team's strikers. “I expect more goals from my centre-halves and central players as well,” he declared. The Senegalese midfielder and the English defender rose to the occasion, earning a fully deserved victory over the opposition's ineffective side.

The Merseyside club's second victory in nine outings was fairly straightforward as the visitors showed why their leading scorer this season is opposition own goals. Apart from a brief flurry in the latter period, the visitors were subdued throughout by Everton’s superior intensity and technical ability. Moyes’ team had three goals disallowed for offside, but a poacher’s finish from the midfielder in added time before the break and the defender's late conversion ensured there would be no reprieve for the former Everton manager.

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 a shot on target after his £27m summer arrival from Villarreal and missed a gilt-edged chance to put his team two goals ahead at Sunderland on Monday. The youngster directed the earliest chance of the game wide of the Fulham keeper's goal frame when picked out by his teammate's fine cross.

Everton controlled the opening stages and the visiting shot-stopper tipped over James Garner’s 30-yard free-kick, given after Sasa Lukic was yellow-carded for fouling the Everton midfielder. The Serbian tripped the same player again before halftime but the referee, the man in charge, rightly ignored home protests for a sending off. The Fulham boss was not risking anything, however, and substituted the player at the break.

Barry believed his luck had changed at last when sliding in at the back post to turn in a low cross by his teammate. But the joy of a maiden strike was erased by an linesman's decision. The attacker was in an illegal position when attacking Gueye’s cross, and failing to connect, and the video assistant referee supported the original call. Barry’s misfortune may have persisted in the final third, but his overall display validated Moyes’ decision to stick with him. His runs and work-rate occupied the opposition's back line and contributed to the hosts the upper hand throughout.

The Londoners grew into the game slowly with the Norwegian and the former Everton midfielder Alex Iwobi working well in midfield, but the early danger from the visitors was minimal. Raúl Jiménez fired weakly at Jordon Pickford when teed up in the box by Iwobi and put a free-kick from a dangerous position directly at the defensive barrier. That summed up their attacking output.

Everton, driven on by Dewsbury-Hall and Ndiaye, had a another strike chalked off for offside when Leno saved a effort from Keane and James Tarkowski volleyed in the loose ball. The home captain had just strayed beyond the last defender when nodding down the winger's cross in the buildup. But the team's third attempt past the keeper did stand. Vitalii Mykolenko delivered a perfect ball to the back post when left unmarked on the left flank by the youngster. The defender met it with a thumping header 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 palpable.

Everton had a further effort ruled out early in the second half after the playmaker scored from a further excellent Mykolenko cross. Ndiaye had cushioned the delivery into Barry, who was offside when challenging the Fulham defender for the touch that reached the home player. The team would have to wait until the closing stages for the security of a two-goal lead. Dewsbury-Hall was the creator with a set-piece that the defender glanced past the goalkeeper. He did so with the back of his shoulder, and Fulham’s appeals for handball were dismissed by the video official.

Silva’s side posed more danger after the introductions of Josh King, the Brazilian and Adama Traoré. The Everton keeper made a fine stop with his legs to prevent Muniz finding the net with his first touch and stopped Traoré with a crucial save late on.