Gueye and Michael Keane find the net as the Toffees overcome the Cottagers

The Everton manager had stressed before the match against Fulham that the responsibility for scoring goals must not rest only on his side's strikers. “I demand more goals from my centre-halves and midfielders as well,” he insisted. The Senegalese midfielder and the English defender responded perfectly, delivering a well-earned victory over Marco Silva’s toothless team.

The Merseyside club's second victory in nine outings was largely untroubled as Fulham showed why their top marksman this season is opposition own goals. Apart from a short spell in the latter period, the visitors were kept quiet all match by the home team's greater urgency and quality. The Blues had three goals disallowed for infringements, but a close-range strike from the midfielder in first-half stoppage time and the defender's late conversion made sure there would be no comeback for the former Everton manager.

No one was more in need of scoring as much as Thierno Barry, the Everton attacker who had gone 10 Premier League outings without a shot on target after his £27m summer arrival from the Spanish side and missed a gilt-edged chance to put his team 2-0 up at the Stadium of Light on Monday. The youngster directed the first opportunity of the game wide of Bernd Leno’s crossbar when found by Iliman Ndiaye’s fine cross.

Everton controlled the opening stages and the Fulham goalkeeper tipped over the midfielder's 30-yard free-kick, awarded after the Fulham player was yellow-carded for fouling the Everton midfielder. The Serbian tripped the identical opponent later in the half but the official, the man in charge, rightly ignored home protests for a sending off. The Fulham boss was taking no further chances, however, and substituted the player at the break.

The striker believed his fortune had finally turned when arriving at the back post to turn in a low cross by his teammate. But the elation of a maiden strike was erased by an linesman's decision. The attacker was offside when attacking the delivery, and missing, and the video assistant referee supported the original call. Barry’s misfortune may have persisted in front of goal, but his overall display justified Moyes’ decision to stick with him. His movement and work-rate kept busy the opposition's back line and helped give Everton the upper hand throughout.

The Londoners came into the contest gradually with the Norwegian and the ex-Goodison player the Nigerian combining effectively in midfield, but the early danger from the away team was minimal. Raúl Jiménez shot tamely at the England keeper when set up in the box by his teammate and put a set-piece from a dangerous position straight into the Everton wall. That summed up their attacking output.

Everton, inspired by the midfielder and the forward, had a second goal disallowed for an infringement when the Fulham goalkeeper saved a effort from Keane and James Tarkowski volleyed in the loose ball. The home captain had just strayed beyond the last defender when heading on Jack Grealish’s delivery in the buildup. But the team's third attempt beating Leno did stand. Vitalii Mykolenko delivered a lovely cross to the far post when left unmarked on the left by Tim Iroegbunam. The defender met it with a thumping header off the crossbar and, though the midfielder mishit the rebound, his teammate the scorer finished from point-blank. The sense of release inside the ground was palpable.

Everton had a further effort ruled out after the restart after the playmaker scored from a further excellent delivery from the left. Ndiaye had laid off the delivery into the striker, who was offside when competing with the Fulham defender for the touch that fell to the home player. Everton would have to wait until the 81st minute for the security of a second goal. Dewsbury-Hall was the architect with a set-piece that Keane glanced past Leno. He scored with the back of his shoulder, and the visitors' protests for a handball were dismissed by VAR.

Fulham carried more of a threat after the introductions of the forward, Rodrigo Muniz and the winger. The Everton keeper made a fine stop with his legs to deny the substitute finding the net with his initial involvement and stopped the speedster with another important stop in the dying moments.