Idrissa Gueye and Michael Keane find the net as the Toffees defeat Fulham

David Moyes had made clear before the match against Fulham that the onus for scoring goals should not fall solely on the team's strikers. “I expect more goals from my defenders and central players as well,” he insisted. Idrissa Gueye and Michael Keane duly obliged, earning a merited victory over the opposition's ineffective team.

The Merseyside club's second win in nine matches was relatively comfortable as Fulham highlighted why their top marksman this season is goals gifted by opponents. Apart from a short spell in the latter period, the away side were kept quiet all match by the home team's greater urgency and quality. Moyes’ team had three efforts disallowed for infringements, but a close-range strike from the midfielder in added time before the break and Keane’s second-half header made sure there would be no comeback for the former Everton manager.

No player needed a goal as much as Thierno Barry, the Everton attacker who had failed to register a shot on target in 10 league games without testing the goalkeeper after his £27m summer arrival from the Spanish side and missed a clear opportunity to put his team two goals ahead at the Stadium of Light on Monday. The youngster headed the earliest chance of the game over Bernd Leno’s goal frame when picked out by Iliman Ndiaye’s fine cross.

The home side dominated the early exchanges and the visiting shot-stopper pushed over James Garner’s 30-yard free-kick, given after the Fulham player was yellow-carded for hauling down the Everton midfielder. Lukic tripped the identical opponent again before halftime but the official, Andrew Madley, correctly waved away home protests for a second yellow. Silva was taking no further chances, however, and withdrew the midfielder at the break.

The striker believed his luck had finally turned when sliding in at the back post to convert a low cross by his teammate. But the joy of a maiden strike was erased by an assistant referee’s flag. The attacker was offside when going for Gueye’s cross, and missing, and the VAR backed up the original call. The forward's bad luck may have continued in the final third, but his overall display justified Moyes’ decision to stick with him. His runs and work-rate occupied Fulham’s central defenders and contributed to the hosts the edge all game.

The Londoners grew into the game gradually with Sander Berge and the former Everton midfielder Alex Iwobi working well in the engine room, but the early danger from the away team was limited. Raúl Jiménez shot tamely at the England keeper when set up in the box by Iwobi and put a set-piece from a promising location directly at the defensive barrier. That summed up their attacking output.

Everton, inspired by the midfielder and the forward, had a another strike disallowed for an infringement when Leno parried a Keane header and the captain fired home the rebound. The home captain had just strayed offside when nodding down Jack Grealish’s cross in the buildup. But the team's next effort past Leno counted. The left-back floated a lovely cross to the far post when found in space on the left flank by the youngster. The defender met it with a thumping header against the bar and, though Iroegbunam mishit the rebound, his teammate Gueye converted from point-blank. The sense of release inside the ground was evident.

The home side had a third goal disallowed early in the second half after the playmaker found the bottom corner from a further excellent Mykolenko cross. Ndiaye had laid off the delivery into the striker, who was offside when challenging the Fulham defender for the touch that reached the home player. Everton would have to be patient until the 81st minute for the comfort of a two-goal lead. The provider was the architect with a corner that Keane directed over Leno. He scored with the upper body, and the visitors' protests for handball were rejected by VAR.

Fulham posed more danger after the substitutions of the forward, the Brazilian and the winger. Pickford made a fine stop with his legs to deny Muniz finding the net with his first touch and denied the speedster with a crucial save in the dying moments.