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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 his side's forwards. “I demand more goals from my centre-halves and midfielders as well,” he declared. Idrissa Gueye and the English defender responded perfectly, delivering a fully deserved victory over the opposition's toothless side.

The Merseyside club's second win in nine outings was fairly straightforward as Fulham showed why their top marksman this season is goals gifted by opponents. Aside from a short spell in the latter period, the visitors were kept quiet throughout by Everton’s greater urgency and quality. Moyes’ team had three goals ruled out for infringements, but a close-range strike from Gueye in first-half stoppage time and Keane’s second-half header ensured there would be no comeback for the former Everton manager.

No one 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 the Spanish side and missed a clear opportunity to put his team two goals ahead at Sunderland on Monday. The youngster headed the earliest chance of the game over the Fulham keeper's crossbar when picked out by Iliman Ndiaye’s excellent delivery.

The home side dominated the early exchanges and the Fulham goalkeeper tipped over James Garner’s 30-yard free-kick, awarded after the Fulham player was booked for fouling Kiernan Dewsbury-Hall. The Serbian brought down the identical opponent later in the half but the official, Andrew Madley, correctly waved away home protests for a sending off. The Fulham boss was not risking anything, however, and withdrew the midfielder at the break.

Barry thought his luck had changed at last when sliding in at the back post to convert a drilled pass by his teammate. But the joy of a first Everton goal was wiped out by an assistant referee’s flag. Ndiaye was offside when attacking Gueye’s cross, and failing to connect, and the video assistant referee backed up the on-field decision. The forward's bad luck may have continued in the final third, but his all-round performance validated the manager's choice to keep the faith. His movement and work-rate kept busy Fulham’s central defenders and contributed to Everton the upper hand throughout.

Fulham came into the contest slowly with the Norwegian and the ex-Goodison player Alex Iwobi working well in the engine room, but the first half threat from the visitors was limited. The Mexican striker shot tamely at Jordon Pickford when set up inside the area by his teammate and sent a free-kick from a dangerous position directly at the defensive barrier. And that was it.

The Blues, driven on by the midfielder and the forward, had a another strike chalked off for offside when Leno saved a effort from Keane and James Tarkowski fired home the loose ball. The skipper had moved offside when heading on Jack Grealish’s cross in the buildup. But the team's third attempt beating Leno counted. Vitalii Mykolenko delivered a lovely cross to the back post when left unmarked on the left flank by Tim Iroegbunam. The defender met it with a thumping header against the bar and, though the midfielder mishit the rebound, his teammate the scorer finished from point-blank. The relief inside the ground was evident.

Everton had a further effort ruled out after the restart after the playmaker scored from another inviting delivery from the left. The attacker had cushioned the delivery into the striker, who was offside when challenging the Fulham defender for the ball that fell to the Everton midfielder. The team would have to wait until the 81st minute for the comfort of a second goal. Dewsbury-Hall was the creator with a corner that Keane directed past Leno. He did so with the upper body, and the visitors' protests for a handball were rejected by VAR.

Silva’s side posed more danger following the substitutions of Josh King, the Brazilian and Adama Traoré. Pickford made a fine stop with his feet to prevent Muniz scoring with his first touch and stopped Traoré with a crucial save in the dying moments.