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The Everton manager had made clear before the match against Fulham that the onus for scoring goals must not fall solely on his side's strikers. “I demand more goals from my centre-halves and central players as well,” he insisted. Idrissa Gueye and Michael Keane rose to the occasion, earning a fully deserved victory over the opposition's toothless side.

Everton’s second victory in nine matches was fairly straightforward as Fulham showed why their leading scorer this season is goals gifted by opponents. Aside from a short spell in the latter period, the visitors were contained throughout by Everton’s greater urgency and quality. The Blues had three efforts ruled out for offside, but a poacher’s finish from Gueye in added time before the break and the defender's second-half header made sure there would be no comeback for their ex-coach.

No player was more in need of scoring as much as Thierno Barry, the Everton attacker who had gone 10 Premier League outings without testing the goalkeeper after his £27m summer arrival from the Spanish side and spurned a clear opportunity to put his team two goals ahead at Sunderland earlier in the week. The youngster headed the first opportunity of the game over Bernd Leno’s goal frame when picked out by Iliman Ndiaye’s excellent delivery.

Everton controlled the early exchanges and the visiting shot-stopper pushed over James Garner’s 30-yard free-kick, given after Sasa Lukic was yellow-carded for hauling down Kiernan Dewsbury-Hall. The Serbian tripped the same player later in the half but the official, the man in charge, correctly waved away home protests for a sending off. The Fulham boss was taking no further chances, however, and withdrew the midfielder at the break.

The striker believed his luck had finally turned when arriving at the far post to convert a low cross by his teammate. But the elation of a maiden strike was erased by an assistant referee’s flag. The attacker was in an illegal position when attacking the delivery, and failing to connect, and the video assistant referee backed up the original call. Barry’s misfortune may have persisted in the final third, but his overall display validated Moyes’ decision to keep the faith. His movement and effort occupied Fulham’s central defenders and contributed to Everton the edge throughout.

Fulham grew into the game gradually with the Norwegian and the former Everton midfielder Alex Iwobi combining effectively in the engine room, but the first half threat from the visitors was minimal. The Mexican striker shot tamely at Jordon Pickford when set up in the box by Iwobi and sent a set-piece from a dangerous position directly at the defensive barrier. That summed up their attacking output.

Everton, inspired by Dewsbury-Hall and Ndiaye, had a another strike disallowed for offside when Leno saved a effort from Keane and the captain volleyed in the loose ball. The skipper had just strayed offside when heading on Jack Grealish’s cross in the buildup. But Everton’s third attempt past the keeper did stand. Vitalii Mykolenko floated a perfect ball to the back post when found in space on the left by the youngster. The defender met it with a thumping header off the crossbar and, though Iroegbunam mishit the rebound, his midfield partner the scorer converted from close range. The sense of release inside Hill Dickinson Stadium was evident.

The home side had a third goal ruled out early in the second half after the playmaker scored from a further excellent delivery from the left. Ndiaye had laid off the delivery into Barry, who was in an offside position when competing with Joachim Anderson for the touch that reached the home player. The team would have to be patient until the closing stages for the comfort of a two-goal lead. Dewsbury-Hall was the architect with a corner that Keane glanced over Leno. He did so with the back of his shoulder, and the visitors' protests for a handball were rejected by VAR.

Fulham carried more of a threat following the substitutions of Josh King, Rodrigo Muniz and the winger. The Everton keeper made a fine stop with his legs to prevent Muniz finding the net with his first touch and denied Traoré with another important stop late on.