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The Everton manager had made clear before the match against Fulham that the responsibility for finding the back of the net must not fall solely on the team's forwards. “I demand more goals from my centre-halves and central players as well,” he declared. The Senegalese midfielder and the English defender responded perfectly, delivering a fully deserved victory over Marco Silva’s toothless team.

The Merseyside club's second victory in nine outings was largely untroubled as the visitors demonstrated why their top marksman this season is opposition own goals. Aside from a short spell in the second half, the away side were contained all match by Everton’s greater urgency and technical ability. Moyes’ team had three efforts disallowed for infringements, but a poacher’s finish from the midfielder in first-half stoppage time and Keane’s late conversion made sure there would be no comeback for the former Everton manager.

No player needed a goal as much as 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 gilt-edged chance to put his team two goals ahead at Sunderland on Monday. The youngster directed the first opportunity of the game wide of the Fulham keeper's goal frame when found by Iliman Ndiaye’s excellent delivery.

Everton controlled the early exchanges and the Fulham goalkeeper tipped over James Garner’s long-range set-piece, awarded after the Fulham player was yellow-carded for hauling down Kiernan Dewsbury-Hall. The Serbian brought down the same player later in the half but the official, the man in charge, rightly ignored home protests for a sending off. The Fulham boss was not risking anything, though, and substituted the player at the break.

The striker believed his fortune had changed at last when arriving at the far post to convert a drilled pass by Gueye. But the joy of a first Everton goal was wiped out by an linesman's decision. Ndiaye was offside when going for the delivery, and missing, and the video assistant referee supported the original call. Barry’s misfortune may have persisted in front of goal, but his all-round performance validated Moyes’ decision to stick with him. His movement and effort occupied the opposition's back line and helped give the hosts the upper hand throughout.

Fulham came into the contest slowly with the Norwegian and the ex-Goodison player the Nigerian combining effectively in the engine room, but the early danger from the visitors was limited. The Mexican striker shot tamely at the England keeper when teed up inside the area by his teammate and sent a free-kick from a promising location straight into the Everton wall. That summed up their attacking output.

Everton, inspired by Dewsbury-Hall and Ndiaye, had a another strike chalked off for an infringement when Leno saved a Keane header and the captain fired home the rebound. The home captain had just strayed offside when nodding down Jack Grealish’s delivery in the buildup. But Everton’s third attempt past the keeper did stand. The left-back floated a perfect ball to the far post when found in space on the left by the youngster. Tarkowski met it with a thumping header off the crossbar and, though Iroegbunam mishit the rebound, his teammate the scorer finished from point-blank. The relief inside Hill Dickinson Stadium was palpable.

Everton had a third goal ruled out after the restart after Dewsbury-Hall scored from a further excellent Mykolenko cross. The attacker had cushioned the delivery into the striker, who was offside when competing with the Fulham defender for the ball that fell to the Everton midfielder. The team would have to wait 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 scored with the upper body, and the visitors' protests for a handball were dismissed by VAR.

Fulham posed more danger following the introductions of the forward, the Brazilian and the winger. The Everton keeper made a fine stop with his feet to prevent Muniz scoring with his first touch and denied the speedster with another important stop in the dying moments.