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David Moyes had stressed before Fulham's visit that the onus for scoring goals must not fall solely on his side's strikers. “I demand more goals from my defenders and midfielders as well,” he stated. Idrissa Gueye and Michael Keane duly obliged, securing a merited victory over the opposition's toothless team.

The Merseyside club's second win in nine outings was largely untroubled as Fulham showed the reason their leading scorer this season is opposition own goals. Apart from a short spell in the second half, the away side were subdued throughout by Everton’s greater urgency and technical ability. The Blues had three efforts disallowed for offside, but a poacher’s finish from the midfielder in first-half stoppage time and the defender's late conversion ensured there would be no reprieve for their ex-coach.

No player was more in need of scoring more than Thierno Barry, the Everton forward who had gone 10 Premier League outings without a shot on target after his £27m summer arrival from the Spanish side and spurned a clear opportunity to put his team two goals ahead at Sunderland on Monday. The 23-year-old directed the earliest chance of the game over Bernd Leno’s crossbar when picked out by Iliman Ndiaye’s excellent delivery.

The home side controlled the opening stages and the Fulham goalkeeper pushed over James Garner’s long-range set-piece, awarded after the Fulham player was booked for fouling Kiernan Dewsbury-Hall. The Serbian tripped the identical opponent later in the half but the referee, the man in charge, rightly ignored Everton appeals for a second yellow. The Fulham boss was not risking anything, however, and withdrew the midfielder at the interval.

Barry thought his luck had changed at last when arriving at the far post to turn in a low cross by his teammate. But the elation of a maiden strike was wiped out by an linesman's decision. Ndiaye was offside when attacking the delivery, and missing, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have persisted in the final third, but his all-round performance justified Moyes’ decision to keep the faith. His runs and work-rate kept busy the opposition's back line and helped give Everton the edge throughout.

Fulham came into the contest gradually with the Norwegian and the former Everton midfielder the Nigerian combining effectively in midfield, but the first half threat from the visitors was limited. The Mexican striker shot tamely at Jordon Pickford when teed up inside the area by Iwobi and sent a set-piece from a dangerous position straight into the Everton wall. And that was it.

The Blues, inspired by the midfielder and the forward, had a second goal disallowed for offside when the Fulham goalkeeper saved a Keane header and the captain volleyed in the loose ball. The skipper had moved offside when nodding down Jack Grealish’s cross in the build-up. But Everton’s next effort beating Leno did stand. Vitalii Mykolenko delivered a perfect ball to the back post when found in space on the left by the youngster. Tarkowski met it with a powerful nod against the bar and, though the midfielder mishit the rebound, his teammate the scorer finished from close range. The relief inside the ground was evident.

The home side had a third goal disallowed after the restart after the playmaker scored from another inviting Mykolenko cross. The attacker had cushioned the delivery into the striker, who was in an offside position when challenging Joachim Anderson for the ball 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 architect with a set-piece that the defender directed past Leno. He scored with the upper body, and the visitors' protests for a handball were rejected by the video official.

Silva’s side posed more danger after the substitutions of Josh King, the Brazilian and Adama Traoré. Pickford saved well with his feet to prevent Muniz finding the net with his first touch and denied the speedster with another important stop late on.