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David Moyes had emphasized 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 demand more goals from my defenders and midfielders as well,” he insisted. Idrissa Gueye and the English defender responded perfectly, earning a fully deserved victory over Marco Silva’s toothless side.

The Merseyside club's second victory in nine outings was largely untroubled as Fulham highlighted the reason their top marksman this season is opposition own goals. Aside from a short spell in the latter period, the visitors were subdued throughout by the home team's superior intensity and technical ability. Moyes’ team had three goals ruled out for offside, but a poacher’s finish from the midfielder in added time before the break and the defender's second-half header made sure there would be no reprieve for their ex-coach.

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 the Spanish side and spurned a gilt-edged chance to put his team 2-0 up at the Stadium of Light on Monday. The 23-year-old headed the earliest chance of the game wide of the Fulham keeper's crossbar when found by Iliman Ndiaye’s excellent delivery.

Everton controlled the early exchanges and the visiting shot-stopper pushed over James Garner’s long-range set-piece, given after the Fulham player was booked for fouling Kiernan Dewsbury-Hall. Lukic tripped the same player later in the half but the official, the man in charge, rightly ignored Everton appeals for a second yellow. The Fulham boss was not risking anything, however, and substituted the midfielder at the interval.

The striker believed his fortune had finally turned when arriving at the back post to convert a drilled pass by his teammate. But the elation of a first Everton goal was wiped out by an assistant referee’s flag. The attacker was offside when attacking Gueye’s cross, and missing, and the VAR backed up the original call. Barry’s misfortune may have continued in front of goal, but his overall display justified the manager's choice to keep the faith. His movement and work-rate kept busy Fulham’s central defenders and contributed to Everton the edge throughout.

The Londoners came into the contest slowly with the Norwegian and the ex-Goodison player the Nigerian working well in midfield, but the first half threat from the away team was limited. Raúl Jiménez shot tamely at the England keeper when set up inside the area by Iwobi and put a free-kick from a dangerous position directly at the defensive barrier. And that was it.

Everton, inspired by Dewsbury-Hall and Ndiaye, had a second goal chalked off for offside when the Fulham goalkeeper parried a Keane header and the captain volleyed in the loose ball. The skipper had just strayed beyond the last defender when nodding down Jack Grealish’s delivery in the buildup. But the team's next effort past Leno counted. The left-back delivered a perfect ball to the back post when left unmarked on the left by the youngster. Tarkowski connected with a powerful nod against the bar and, though the midfielder fluffed his lines, his midfield partner Gueye converted from close range. The sense of release inside the ground was palpable.

The home side had a further effort ruled out early in the second half after the playmaker scored from another inviting delivery from the left. The attacker had cushioned the delivery into the striker, who was offside when challenging the Fulham defender for the touch that reached the home player. The team would have to be patient until the closing stages for the security of a two-goal lead. Dewsbury-Hall was the architect with a corner that the defender glanced past the goalkeeper. He scored with the upper body, and the visitors' protests for a handball were rejected by VAR.

Fulham posed more danger following the introductions of the forward, the Brazilian and Adama Traoré. Pickford made a fine stop with his legs to prevent Muniz scoring with his first touch and denied the speedster with another important stop in the dying moments.