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The Everton manager had made clear before Fulham's visit that the onus for finding the back of the net must not rest only on his side's strikers. “I demand more goals from my centre-halves and midfielders as well,” he declared. Idrissa Gueye and Michael Keane rose to the occasion, securing a merited victory over the opposition's toothless team.

Everton’s second victory in nine matches was largely untroubled as the visitors demonstrated the reason their top marksman this season is opposition own goals. Aside from a brief flurry in the latter period, the away side were kept quiet throughout by Everton’s superior intensity and technical ability. Moyes’ team had three efforts disallowed for offside, but a poacher’s finish from the midfielder in first-half stoppage time and the defender's second-half header ensured there would be no reprieve for the former Everton manager.

No one was more in need of scoring more than Thierno Barry, the Goodison Park attacker who had failed to register a shot on target in 10 league games without a shot on target after his £27m summer arrival from Villarreal and spurned a clear opportunity to put his team two goals ahead at Sunderland on Monday. The youngster headed the earliest chance of the game over Bernd Leno’s crossbar when picked out by Iliman Ndiaye’s fine cross.

The home side dominated the early exchanges and the visiting shot-stopper pushed over the midfielder's 30-yard free-kick, given after the Fulham player was yellow-carded for hauling down Kiernan Dewsbury-Hall. Lukic tripped the identical opponent later in the half but the official, the man in charge, correctly waved away home protests for a sending off. Silva was not risking anything, however, and substituted the player at the interval.

Barry thought his luck had finally turned when arriving at the back post to convert a drilled pass by his teammate. But the elation of a first Everton goal was erased by an linesman's decision. Ndiaye was offside when going for Gueye’s cross, and failing to connect, and the VAR backed up the on-field decision. The forward's bad luck may have continued in front of goal, but his all-round performance validated Moyes’ decision to keep the faith. His runs and work-rate occupied Fulham’s central defenders and contributed to Everton the upper hand all game.

The Londoners grew into the game gradually with the Norwegian and the former Everton midfielder the Nigerian combining effectively in the engine room, but the first half threat from the visitors was limited. The Mexican striker fired weakly at the England keeper when teed up inside the area by Iwobi and put a set-piece from a promising location straight into the defensive barrier. And that was it.

Everton, driven on by the midfielder and Ndiaye, had a second goal disallowed for an infringement when Leno saved a Keane header and the captain fired home the loose ball. The skipper had just strayed offside when nodding down Jack Grealish’s cross in the buildup. But the team's third attempt beating Leno counted. The left-back delivered a lovely cross 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 Iroegbunam fluffed his lines, his teammate the scorer converted from point-blank. The relief inside the ground was palpable.

The home side had a third goal ruled out early in the second half after Dewsbury-Hall found the bottom corner from a further excellent delivery from the left. Ndiaye had cushioned the ball into the striker, who was offside when competing with Joachim Anderson for the ball that reached the home player. Everton would have to be patient until the closing stages for the security of a two-goal lead. The provider was the creator with a corner that the defender directed over the goalkeeper. He scored with the back of his shoulder, and Fulham’s appeals for a handball were dismissed by the video official.

Fulham posed more danger after the introductions of the forward, Rodrigo Muniz and the winger. The Everton keeper saved well with his feet to prevent Muniz scoring with his first touch and denied the speedster with a crucial save late on.