Gueye and Michael Keane on target as the Toffees overcome the Cottagers

David Moyes had stressed before the match against Fulham that the onus for scoring goals must not rest only on his side's forwards. “I demand more goals from my defenders and midfielders as well,” he insisted. Idrissa Gueye and the English defender duly obliged, securing a merited victory over Marco Silva’s ineffective team.

The Merseyside club's second win in nine outings was relatively comfortable as the visitors demonstrated the reason their leading scorer this season is opposition own goals. Apart from a short spell in the latter period, the away side were kept quiet throughout by Everton’s greater urgency and technical ability. Moyes’ team had three goals disallowed for offside, but a close-range strike from Gueye in first-half stoppage time and Keane’s late conversion made sure there would be no comeback for their ex-coach.

No one was more in need of scoring as much as Thierno Barry, the Goodison Park 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 two goals ahead at the Stadium of Light earlier in the week. The youngster directed the earliest chance of the game wide of Bernd Leno’s crossbar when found by his teammate's excellent delivery.

Everton controlled the opening stages and the visiting shot-stopper tipped over the midfielder's 30-yard free-kick, awarded after Sasa Lukic was booked for fouling Kiernan Dewsbury-Hall. Lukic brought down the same player again before halftime but the official, Andrew Madley, rightly ignored Everton appeals for a second yellow. Silva was taking no further chances, however, and withdrew the player at the break.

The striker believed his fortune had finally turned when sliding in at the back post to turn in a drilled pass by Gueye. But the elation of a maiden strike was wiped out by an assistant referee’s flag. Ndiaye was in an illegal position when attacking the delivery, and failing to connect, and the video assistant referee supported the on-field decision. Barry’s misfortune may have persisted in the final third, but his all-round performance justified the manager's choice to stick with him. His runs and effort occupied the opposition's back line and helped give Everton the upper hand all game.

The Londoners grew into the game slowly with Sander Berge and the former Everton midfielder Alex Iwobi working well in midfield, but the first half threat from the visitors was minimal. Raúl Jiménez fired weakly at Jordon Pickford when set up inside the area by Iwobi and put a free-kick from a dangerous position straight into the Everton wall. That summed up their attacking output.

The Blues, driven on by Dewsbury-Hall and the forward, had a second goal disallowed for an infringement when Leno parried a Keane header and the captain fired home the loose ball. The home captain had moved offside when heading on the winger's cross in the buildup. But the team's next effort beating the keeper did stand. Vitalii Mykolenko floated a perfect ball to the back post when left unmarked on the left flank by Tim Iroegbunam. The defender connected with a thumping header against the bar and, though the midfielder fluffed his lines, his midfield partner Gueye finished from point-blank. The sense of release inside the ground was palpable.

Everton had a third goal disallowed early in the second half after Dewsbury-Hall found the bottom corner from a further excellent delivery from the left. The attacker had cushioned the delivery into the striker, who was in an offside position when challenging Joachim Anderson for the touch that reached the Everton midfielder. Everton would have to be patient until the 81st minute for the security of a two-goal lead. The provider was the creator with a corner that the defender directed past Leno. He did so with the upper body, and the visitors' protests for a handball were dismissed by the video official.

Silva’s side posed more danger after the introductions of the forward, the Brazilian and the winger. Pickford saved well with his legs to prevent the substitute scoring with his initial involvement and denied Traoré with a crucial save in the dying moments.