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

David Moyes had stressed before the match against Fulham that the onus for scoring goals must not fall solely on the team's forwards. “I want more goals from my centre-halves and midfielders as well,” he insisted. The Senegalese midfielder and the English defender duly obliged, earning a fully deserved victory over Marco Silva’s ineffective side.

Everton’s second victory in nine matches was largely untroubled as the visitors highlighted why their top marksman this season is goals gifted by opponents. Apart from a brief flurry in the second half, the visitors were kept quiet all match by the home team's superior intensity and technical ability. Moyes’ team had three goals ruled out for offside, but a close-range strike from the midfielder in added time before the break 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 as much as the young striker, the Goodison Park forward who had failed to register a shot on target in 10 league games without a shot on target after his £27m summer arrival from the Spanish side and missed a clear opportunity to put his team two goals ahead at Sunderland on Monday. The 23-year-old directed the first opportunity of the game wide of the Fulham keeper's crossbar when found by his teammate's fine cross.

Everton controlled the early exchanges and the visiting shot-stopper tipped over James Garner’s long-range set-piece, awarded after Sasa Lukic was yellow-carded for hauling down the Everton midfielder. Lukic brought down the identical opponent later in the half but the official, Andrew Madley, rightly ignored Everton appeals for a second yellow. Silva was taking no further chances, however, and substituted the player at the interval.

The striker believed his fortune had changed at last when sliding in at the back post to convert a low cross by Gueye. But the elation of a maiden strike was wiped out by an linesman's decision. The attacker was in an illegal position when going for Gueye’s cross, and failing to connect, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have continued in front of goal, but his overall display validated the manager's choice to keep the faith. His runs and work-rate kept busy the opposition's back line and helped give the hosts the upper hand throughout.

Fulham grew into the game gradually with Sander Berge and the ex-Goodison player Alex Iwobi working well in midfield, but the first half threat from the away team was minimal. The Mexican striker fired weakly at the England keeper when teed up inside the area by Iwobi and put a set-piece from a dangerous position straight into the defensive barrier. And that was it.

Everton, driven on by the midfielder and the forward, had a second goal disallowed for an infringement when the Fulham goalkeeper saved a Keane header and James Tarkowski volleyed in the loose ball. The skipper had just strayed beyond the last defender when heading on the winger's delivery in the build-up. But the team's third attempt beating the keeper did stand. The left-back floated a perfect ball to the far post when found in space on the left flank by the youngster. The defender connected with a powerful nod off the crossbar and, though Iroegbunam fluffed his lines, his teammate Gueye converted from close range. The relief inside the ground was evident.

Everton had a further effort disallowed early in the second half after Dewsbury-Hall scored from another inviting delivery from the left. The attacker had cushioned the delivery into Barry, who was in an offside position when challenging Joachim Anderson for the touch that reached the home player. The team would have to be patient until the 81st minute for the security of a two-goal lead. Dewsbury-Hall was the creator with a corner that the defender directed over the goalkeeper. He scored with the upper body, and the visitors' protests for a handball were rejected by VAR.

Fulham carried more of a threat after the introductions of the forward, Rodrigo Muniz and the winger. Pickford saved well with his feet to deny Muniz scoring with his first touch and denied the speedster with a crucial save in the dying moments.