Idrissa Gueye and Keane find the net as the Toffees overcome the Cottagers

David Moyes had stressed before the match against Fulham that the onus for finding the back of the net must not fall solely on the team's forwards. “I expect more goals from my centre-halves and midfielders as well,” he declared. Idrissa Gueye and Michael Keane duly obliged, delivering a fully deserved victory over the opposition's toothless side.

Everton’s second win in nine outings was largely untroubled as the visitors showed the reason their top marksman this season is goals gifted by opponents. Apart 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 ruled out for offside, but a close-range strike from Gueye in first-half stoppage time and Keane’s late conversion made sure there would be no reprieve for their ex-coach.

No player was more in need of scoring as much as Thierno Barry, the Goodison Park attacker who had gone 10 Premier League outings without a shot on target after his £27m summer arrival from Villarreal and missed a clear opportunity to put his team 2-0 up at Sunderland on Monday. The 23-year-old headed the first opportunity of the game over the Fulham keeper's crossbar when picked out by his teammate's excellent delivery.

The home side dominated the early exchanges and the visiting shot-stopper pushed over James Garner’s long-range set-piece, awarded after Sasa Lukic was yellow-carded for hauling down the Everton midfielder. The Serbian tripped the identical opponent later in the half but the official, the man in charge, rightly ignored Everton appeals for a sending off. The Fulham boss was taking no further chances, though, and substituted the midfielder at the break.

The striker thought his fortune had changed at last when sliding in at the far post to convert a drilled pass by Gueye. But the joy of a maiden strike was erased by an assistant referee’s flag. The attacker was offside when attacking the delivery, and failing to connect, and the video assistant referee backed up the on-field decision. The forward's bad luck may have continued in front of goal, but his overall display justified Moyes’ decision to keep the faith. His movement and work-rate occupied Fulham’s central defenders and contributed to Everton the upper hand all game.

Fulham grew into the game gradually with Sander Berge and the former Everton midfielder Alex Iwobi combining effectively in the engine room, but the early danger from the visitors was limited. The Mexican striker fired weakly at Jordon Pickford when teed up in the box by Iwobi and sent a set-piece from a dangerous position straight into the Everton wall. That summed up their attacking output.

Everton, inspired by Dewsbury-Hall and Ndiaye, had a second goal chalked off for an infringement when Leno saved a effort from Keane and James Tarkowski fired home the rebound. The skipper had moved offside when heading on the winger's cross in the build-up. But Everton’s third attempt past the keeper counted. The left-back floated a perfect ball to the back post when left unmarked on the left flank by the youngster. The defender connected with a thumping header against the bar and, though Iroegbunam fluffed his lines, his teammate Gueye finished from close range. The relief inside the ground was palpable.

Everton had a third goal disallowed early in the second half after the playmaker scored from another inviting Mykolenko cross. The attacker had laid off the ball into the striker, who was offside when competing with the Fulham defender for the ball that fell to the home player. Everton would have to wait until the closing stages for the comfort of a second goal. The provider was the creator with a corner that Keane glanced past the goalkeeper. He did so with the back of his shoulder, and Fulham’s appeals for handball were dismissed by VAR.

Fulham posed more danger following the substitutions of the forward, Rodrigo Muniz and the winger. The Everton keeper saved well with his feet to prevent Muniz finding the net with his first touch and stopped the speedster with another important stop in the dying moments.