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David Moyes had stressed before Fulham's visit that the onus for finding the back of the net should not rest only on the team's forwards. “I demand more goals from my defenders and central players as well,” he declared. Idrissa Gueye and the English defender responded perfectly, securing a well-earned victory over Marco Silva’s toothless team.

The Merseyside club's second win in nine outings was largely untroubled as Fulham demonstrated the reason their leading scorer this season is goals gifted by opponents. Apart from a short spell in the second half, the visitors were subdued throughout by Everton’s greater urgency and quality. The Blues had three efforts ruled out for infringements, but a poacher’s finish from Gueye in first-half stoppage time and the defender's second-half header made sure there would be no comeback for their ex-coach.

No player needed a goal as much as Thierno Barry, the Everton attacker who had failed to register a shot on target in 10 league games without testing the goalkeeper after his £27m summer arrival from Villarreal and missed a gilt-edged chance to put his team 2-0 up at the Stadium of Light earlier in the week. The youngster headed the first opportunity of the game wide of the Fulham keeper's crossbar when found by Iliman Ndiaye’s fine cross.

Everton controlled the opening stages and the visiting shot-stopper pushed over the midfielder's 30-yard free-kick, given after Sasa Lukic was yellow-carded for fouling Kiernan Dewsbury-Hall. The Serbian tripped the same player later in the half but the referee, Andrew Madley, correctly waved away Everton appeals for a second yellow. Silva was not risking anything, however, and substituted the player at the interval.

Barry thought his luck had changed at last when sliding in at the far post to convert a low cross by Gueye. But the joy of a first Everton goal was wiped out by an assistant referee’s flag. Ndiaye was offside when going for Gueye’s cross, and missing, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have continued in the final third, but his all-round performance validated the manager's choice to keep the faith. His movement and effort kept busy the opposition's back line and contributed to Everton the edge throughout.

The Londoners grew into the game slowly with the Norwegian and the former Everton midfielder Alex Iwobi working well in the engine room, but the first half threat from the visitors was limited. Raúl Jiménez fired weakly at Jordon Pickford when set up inside the area by his teammate and sent a set-piece from a dangerous position straight into the defensive barrier. And that was it.

The Blues, inspired by Dewsbury-Hall and the forward, had a another strike disallowed for an infringement when the Fulham goalkeeper saved a effort from Keane and James Tarkowski fired home the loose ball. The skipper had just strayed beyond the last defender when heading on the winger's delivery in the build-up. But the team's third attempt past the keeper did stand. The left-back delivered a perfect ball to the far post when left unmarked on the left flank by the youngster. The defender met it with a powerful nod against the bar and, though the midfielder fluffed his lines, his teammate Gueye converted from close range. The sense of release inside the ground was evident.

Everton had a further effort ruled out early in the second half after the playmaker scored from a further excellent delivery from the left. The attacker had laid off the delivery into the striker, who was in an offside position when challenging Joachim Anderson for the ball that fell to the home player. The team would have to wait until the 81st minute for the comfort of a second goal. Dewsbury-Hall was the architect 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 a handball were dismissed by the video official.

Fulham posed more danger after the substitutions of Josh King, the Brazilian and the winger. The Everton keeper saved well with his legs to deny Muniz finding the net with his first touch and denied Traoré with another important stop late on.