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David Moyes had made clear before Fulham's visit that the onus for finding the back of the net should not fall solely on the team's forwards. “I demand more goals from my defenders and midfielders as well,” he declared. Idrissa Gueye and Michael Keane duly obliged, delivering a merited victory over Marco Silva’s toothless team.

Everton’s second win in nine outings was fairly straightforward as the visitors demonstrated why their leading scorer this season is goals gifted by opponents. Aside from a short spell in the latter period, the away side were contained all match by the home team's greater urgency and quality. Moyes’ team had three efforts ruled out for infringements, but a close-range strike from Gueye in added time before the break and Keane’s late conversion ensured there would be no reprieve for the former Everton manager.

No player was more in need of scoring more than Thierno Barry, the Everton forward who had failed to register a shot on target in 10 league games 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 over the Fulham keeper's crossbar when picked out by his teammate's excellent delivery.

Everton dominated the opening stages and the visiting shot-stopper pushed over James Garner’s 30-yard free-kick, given after the Fulham player was yellow-carded for fouling Kiernan Dewsbury-Hall. Lukic tripped the identical opponent again before halftime but the official, Andrew Madley, rightly ignored Everton appeals for a sending off. The Fulham boss was not risking anything, though, and substituted the midfielder at the break.

Barry believed his fortune had changed at last when arriving at the back post to turn in a drilled pass by Gueye. But the joy of a first Everton goal was wiped out by an linesman's decision. The attacker was in an illegal position when going for the delivery, and missing, and the VAR supported the original call. The forward's bad luck may have continued in front of goal, but his all-round performance justified Moyes’ decision to stick with him. His movement and effort occupied Fulham’s central defenders and contributed to Everton the upper hand throughout.

The Londoners grew into the game slowly with the Norwegian and the ex-Goodison player Alex Iwobi working well in midfield, but the early danger from the visitors was limited. The Mexican striker shot tamely at Jordon Pickford when teed up inside the area by his teammate and put a set-piece from a promising location straight into the Everton wall. And that was it.

Everton, inspired by the midfielder and the forward, had a another strike chalked off for an infringement when Leno parried a effort from Keane and the captain volleyed in the rebound. The skipper had just strayed beyond the last defender when nodding down the winger's cross in the build-up. But the team's third attempt past Leno counted. The left-back delivered a perfect ball to the back post when left unmarked on the left by Tim Iroegbunam. Tarkowski met it with a thumping header against the bar and, though the midfielder mishit the rebound, his midfield partner Gueye finished from close range. The sense of release inside Hill Dickinson Stadium was evident.

The home side had a further effort disallowed after the restart after the playmaker found the bottom corner from a further excellent Mykolenko cross. The attacker had cushioned the delivery into Barry, who was offside when competing with Joachim Anderson for the touch that fell to the home player. Everton would have to be patient until the closing stages for the comfort of a two-goal lead. The provider was the architect with a corner that Keane glanced over the goalkeeper. He did so with the back of his shoulder, and Fulham’s appeals for handball were rejected by the video official.

Fulham posed more danger following the substitutions of the forward, the Brazilian and Adama Traoré. The Everton keeper made a fine stop with his legs to deny the substitute scoring with his first touch and denied Traoré with a crucial save late on.