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David Moyes had stressed before Fulham's visit that the onus for finding the back of the net should not fall solely on his side's strikers. “I demand more goals from my centre-halves and central players as well,” he declared. Idrissa Gueye and Michael Keane responded perfectly, earning a well-earned victory over the opposition's toothless side.

The Merseyside club's second victory in nine outings was largely untroubled as the visitors highlighted the reason their leading scorer this season is goals gifted by opponents. Aside from a short spell in the latter period, the visitors were kept quiet all match by the home team's greater urgency and technical ability. The Blues had three efforts ruled out for infringements, but a poacher’s finish from Gueye in first-half stoppage time and Keane’s second-half header made sure there would be no reprieve for their ex-coach.

No one needed a goal more than Thierno Barry, the Everton forward who had gone 10 Premier League outings without testing the goalkeeper after his £27m summer arrival from Villarreal and missed a clear opportunity to put his team 2-0 up at Sunderland on Monday. The youngster directed the first opportunity of the game wide of Bernd Leno’s crossbar when found by his teammate's excellent delivery.

Everton controlled the opening stages and the visiting shot-stopper pushed over James Garner’s long-range set-piece, awarded after the Fulham player was booked for fouling Kiernan Dewsbury-Hall. Lukic brought down the same player later in the half but the official, Andrew Madley, rightly ignored Everton appeals for a second yellow. The Fulham boss was taking no further chances, though, and withdrew the player at the interval.

Barry believed his luck had changed at last when arriving at the far post to convert a drilled pass by Gueye. But the joy of a first Everton goal was erased by an assistant referee’s flag. The attacker was in an illegal position when going for the delivery, and missing, and the video assistant referee supported the original call. 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 effort kept busy Fulham’s central defenders and helped give the hosts the edge throughout.

The Londoners grew into the game gradually with the Norwegian and the former Everton midfielder Alex Iwobi working well in midfield, but the first half threat from the away team was minimal. The Mexican striker shot tamely at the England keeper when teed up in the box by Iwobi and sent a set-piece from a promising location straight into the defensive barrier. That summed up their attacking output.

The Blues, driven on by the midfielder and the forward, had a another strike disallowed for offside when Leno saved a effort from Keane and James Tarkowski volleyed in the rebound. The home captain had just strayed offside when nodding down Jack Grealish’s cross in the buildup. But Everton’s next effort beating Leno did stand. Vitalii Mykolenko delivered a perfect ball to the back post when left unmarked on the left flank by the youngster. Tarkowski connected with a powerful nod off the crossbar and, though Iroegbunam mishit the rebound, his teammate Gueye finished from point-blank. The relief inside the ground was palpable.

Everton had a further effort ruled out early in the second half after Dewsbury-Hall scored from another inviting 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 security of a two-goal lead. The provider was the creator with a corner that Keane glanced over Leno. He scored with the back of his shoulder, and the visitors' protests for a handball were dismissed by the video official.

Fulham carried more of a threat after the introductions of the forward, Rodrigo Muniz and the winger. Pickford made a fine stop with his feet to prevent the substitute finding the net with his initial involvement and stopped the speedster with a crucial save late on.