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David Moyes had stressed before Fulham's visit that the responsibility for finding the back of the net should not fall solely on his side's forwards. “I demand more goals from my defenders and midfielders as well,” he insisted. Idrissa Gueye and the English defender responded perfectly, earning a well-earned victory over the opposition's toothless side.

The Merseyside club's second win in nine matches was relatively comfortable as the visitors showed the reason 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 the home team's greater urgency and technical ability. Moyes’ team had three goals ruled out for offside, but a close-range strike from the midfielder in first-half stoppage time and the defender's second-half header ensured there would be no comeback for their ex-coach.

No player was more in need of scoring more than the young striker, the Everton attacker who had gone 10 Premier League outings without a shot on target after his big-money move from the Spanish side and spurned a clear opportunity to put his team 2-0 up at Sunderland on Monday. The 23-year-old headed the earliest chance of the game over Bernd Leno’s crossbar when picked out by Iliman Ndiaye’s fine cross.

Everton dominated the early exchanges and the Fulham goalkeeper tipped over the midfielder's 30-yard free-kick, given after Sasa Lukic was booked for hauling down the Everton midfielder. The Serbian brought down the same player later in the half but the referee, the man in charge, rightly ignored Everton appeals for a second yellow. Silva was not risking anything, though, and withdrew the midfielder at the break.

Barry believed his fortune had finally turned when sliding in at the far post to turn in a low cross by Gueye. But the joy of a first Everton goal was erased by an assistant referee’s flag. The attacker was offside when attacking Gueye’s cross, and missing, and the VAR supported the original call. Barry’s misfortune may have continued in the final third, but his all-round performance justified the manager's choice to keep the faith. His movement and work-rate kept busy Fulham’s central defenders and helped give Everton the upper hand throughout.

The Londoners grew into the game gradually with Sander Berge and the former Everton midfielder Alex Iwobi combining effectively in the engine room, but the first half threat from the away team was limited. Raúl Jiménez shot tamely at Jordon Pickford when teed up in the box by his teammate and put a set-piece from a dangerous position directly at the Everton wall. And that was it.

The Blues, inspired by the midfielder and the forward, had a another strike disallowed for an infringement when the Fulham goalkeeper saved a Keane header and the captain fired home the loose ball. The skipper had just strayed beyond the last defender when heading on Jack Grealish’s cross in the build-up. But the team's next effort past Leno did stand. Vitalii Mykolenko floated a perfect ball to the far post when left unmarked on the left by the youngster. Tarkowski met it with a powerful nod off the crossbar and, though Iroegbunam fluffed his lines, his midfield partner Gueye converted from close range. The relief inside Hill Dickinson Stadium was palpable.

The home side had a further effort disallowed after the restart after Dewsbury-Hall scored from a further excellent Mykolenko cross. The attacker had laid off the ball into the striker, who was in an offside position when competing with the Fulham defender for the ball that reached the Everton midfielder. Everton would have to be patient until the closing stages for the security of a two-goal lead. The provider was the architect with a corner 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.

Fulham carried more of a threat after the substitutions of Josh King, Rodrigo Muniz and Adama Traoré. Pickford saved well with his legs to deny Muniz finding the net with his first touch and stopped Traoré with another important stop in the dying moments.