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David Moyes had stressed before Fulham's visit that the responsibility for finding the back of the net should not rest only on his side's forwards. “I demand more goals from my defenders and central players as well,” he declared. The Senegalese midfielder and the English defender duly obliged, delivering a fully deserved victory over the opposition's ineffective side.

The Merseyside club's second win in nine outings was relatively comfortable as the visitors highlighted the reason their top marksman this season is goals gifted by opponents. Aside from a short spell in the latter period, the visitors were subdued throughout by Everton’s greater urgency and quality. The Blues had three efforts ruled out for offside, but a poacher’s finish from the midfielder in first-half stoppage time and the defender's second-half header ensured there would be no comeback for the former Everton manager.

No one needed a goal more than Thierno Barry, the Everton attacker who had gone 10 Premier League outings without testing the goalkeeper after his big-money move from Villarreal and missed a clear opportunity to put his team two goals ahead at Sunderland on Monday. The youngster headed the first opportunity of the game wide of Bernd Leno’s goal frame when found by his teammate's excellent delivery.

The home side controlled the early exchanges and the visiting shot-stopper pushed over James Garner’s 30-yard free-kick, awarded after Sasa Lukic was yellow-carded for hauling down the Everton midfielder. The Serbian brought down the same player later in the half but the referee, Andrew Madley, rightly ignored Everton appeals for a second yellow. The Fulham boss was taking no further chances, however, and substituted the midfielder at the interval.

Barry thought his luck had changed at last when sliding in at the far post to convert a drilled pass by Gueye. 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 on-field decision. The forward's bad luck may have continued in front of goal, but his overall display justified the manager's choice to keep the faith. His runs and work-rate occupied the opposition's back line and helped give Everton the upper hand throughout.

Fulham grew into the game slowly with Sander Berge and the former Everton midfielder Alex Iwobi working well in midfield, but the early danger from the visitors was limited. Raúl Jiménez shot tamely at the England keeper when set up inside the area by his teammate and sent a set-piece from a promising location directly at the defensive barrier. That summed up their attacking output.

Everton, inspired by Dewsbury-Hall and Ndiaye, had a another strike disallowed for an infringement when the Fulham goalkeeper saved a effort from Keane and the captain fired home the rebound. The skipper had just strayed offside when heading on the winger's cross in the buildup. But the team's next effort past Leno did stand. Vitalii Mykolenko delivered a lovely cross to the back post when left unmarked on the left flank by the youngster. The defender connected with a powerful nod against the bar and, though Iroegbunam fluffed his lines, his teammate the scorer converted from close range. The sense of release inside Hill Dickinson Stadium was evident.

The home side had a further effort disallowed after the restart after Dewsbury-Hall scored from another inviting Mykolenko cross. Ndiaye had cushioned the delivery into the striker, who was in an offside position when competing with Joachim Anderson for the touch that reached the Everton midfielder. Everton would have to be patient until the closing stages for the security of a two-goal lead. Dewsbury-Hall was the architect with a corner that the defender glanced over the goalkeeper. He scored with the upper body, and Fulham’s appeals for handball were dismissed by the video official.

Silva’s side posed more danger after the substitutions of the forward, Rodrigo Muniz and the winger. Pickford made a fine stop with his feet to prevent Muniz finding the net with his first touch and denied the speedster with a crucial save late on.