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David Moyes had stressed before the match against Fulham that the responsibility for scoring goals should not fall solely on the team's forwards. “I demand more goals from my centre-halves and central players as well,” he insisted. The Senegalese midfielder and the English defender rose to the occasion, securing a merited victory over the opposition's toothless side.

The Merseyside club's second win in nine outings was largely untroubled as the visitors showed the reason their top marksman this season is opposition own goals. Apart from a short spell in the second half, the visitors were subdued all match by Everton’s greater urgency and quality. Moyes’ team had three goals disallowed for offside, but a poacher’s finish from the midfielder in added time before the break and Keane’s second-half header made sure there would be no reprieve for the former Everton manager.

No player was more in need of scoring more than Thierno Barry, the Goodison Park 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 gilt-edged chance to put his team two goals ahead at Sunderland on Monday. The youngster headed the first opportunity of the game wide of the Fulham keeper's crossbar when found by Iliman Ndiaye’s fine cross.

Everton dominated the opening stages and the Fulham goalkeeper tipped over the midfielder's 30-yard free-kick, given after the Fulham player was booked for hauling down the Everton midfielder. The Serbian tripped the identical opponent again before halftime but the referee, the man in charge, rightly ignored home protests for a second yellow. The Fulham boss was taking no further chances, though, and withdrew the player at the break.

Barry thought his fortune had changed at last when sliding in at the far post to convert a low cross by Gueye. But the joy of a maiden strike was wiped out by an assistant referee’s flag. Ndiaye was offside when going for the delivery, and failing to connect, and the VAR supported the on-field decision. The forward's bad luck may have continued in front of goal, but his overall display validated Moyes’ decision to stick with him. His movement and work-rate occupied Fulham’s central defenders and contributed to the hosts 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 first half threat from the away team was minimal. Raúl Jiménez shot tamely at the England keeper when teed up inside the area by his teammate and put a set-piece from a promising location directly at the Everton wall. And that was it.

The Blues, inspired by Dewsbury-Hall and the forward, had a second goal chalked off for offside when Leno saved a effort from Keane and the captain fired home the rebound. The skipper had moved offside when nodding down Jack Grealish’s cross in the build-up. But Everton’s third attempt past Leno did stand. The left-back delivered a perfect ball to the far post when found in space on the left by the youngster. Tarkowski met it with a powerful nod against the bar and, though the midfielder fluffed his lines, his teammate the scorer finished from point-blank. The sense of release inside the ground was palpable.

The home side had a third goal ruled out after the restart after Dewsbury-Hall scored from a further excellent Mykolenko cross. Ndiaye had cushioned the ball into the striker, who was offside when competing with Joachim Anderson for the ball that fell to the home player. The team would have to be patient until the 81st minute for the comfort of a second goal. The provider was the architect with a set-piece that Keane directed over Leno. He did so with the back of his shoulder, and the visitors' protests for handball were dismissed by VAR.

Fulham posed more danger following the introductions of the forward, Rodrigo Muniz and the winger. The Everton keeper saved well with his feet to prevent the substitute finding the net with his initial involvement and stopped Traoré with another important stop in the dying moments.