Idrissa Gueye along with Michael Keane on target as the Toffees sink the Cottagers

The Everton manager had stressed before the match against Fulham that the responsibility for finding the back of the net must not rest only on his side's strikers. “I demand more goals from my centre-halves and midfielders as well,” he insisted. Idrissa Gueye and Michael Keane responded perfectly, securing a merited victory over Marco Silva’s ineffective team.

Everton’s second win in nine matches was fairly straightforward as Fulham demonstrated the reason their top marksman this season is opposition own goals. Aside from a short spell in the second half, the visitors were kept quiet throughout by the home team's greater urgency and technical ability. The Blues had three goals ruled out for infringements, but a poacher’s finish from Gueye in first-half stoppage time and Keane’s late conversion made sure there would be no comeback for their ex-coach.

No player 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 Villarreal and missed a gilt-edged chance to put his team 2-0 up at the Stadium of Light on Monday. The 23-year-old directed the earliest chance of the game over Bernd Leno’s goal frame when found by Iliman Ndiaye’s fine cross.

Everton controlled the early exchanges and the visiting shot-stopper pushed over the midfielder's long-range set-piece, awarded after Sasa Lukic was booked for fouling the Everton midfielder. The Serbian brought down the same player again before halftime but the referee, the man in charge, rightly ignored home protests for a second yellow. Silva was taking no further chances, however, and withdrew the player at the break.

Barry believed his luck had finally turned when arriving at the far post to convert a low cross by his teammate. But the joy of a first Everton goal was erased by an assistant referee’s flag. Ndiaye was offside when attacking Gueye’s cross, and missing, and the video assistant referee backed up the on-field decision. The forward's bad luck may have persisted in front of goal, but his all-round performance justified the manager's choice to keep the faith. His movement and effort kept busy Fulham’s central defenders and contributed to Everton the edge all game.

The Londoners came into the contest slowly with the Norwegian and the ex-Goodison player Alex Iwobi combining effectively in the engine room, but the early danger from the away team was limited. Raúl Jiménez fired weakly at the England keeper when teed up inside the area by Iwobi and sent a free-kick from a dangerous position straight into the defensive barrier. That summed up their attacking output.

Everton, inspired by Dewsbury-Hall and the forward, had a another strike chalked off for offside when Leno parried a Keane header and the captain fired home the rebound. The home captain had moved beyond the last defender when nodding down Jack Grealish’s cross in the build-up. But Everton’s third attempt beating the keeper did stand. The left-back floated a lovely cross to the back post when left unmarked on the left by the youngster. Tarkowski connected with a powerful nod against the bar and, though Iroegbunam fluffed his lines, his midfield partner the scorer finished from close range. The sense of release inside Hill Dickinson Stadium was palpable.

Everton had a third goal disallowed after the restart after Dewsbury-Hall scored from a further excellent Mykolenko cross. The attacker had cushioned the ball into Barry, who was in an offside position when competing with Joachim Anderson for the touch that reached the home player. The team would have to wait until the 81st minute for the comfort of a two-goal lead. The provider was the creator with a corner that the defender directed past Leno. He scored with the back of his shoulder, and the visitors' protests for handball were rejected by the video official.

Fulham carried more of a threat following the substitutions of the forward, the Brazilian and the winger. Pickford saved well with his feet to deny Muniz finding the net with his first touch and stopped the speedster with another important stop in the dying moments.