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David Moyes had made clear before Fulham's visit that the responsibility for scoring goals should not fall solely on the team's forwards. “I expect more goals from my centre-halves and midfielders as well,” he declared. The Senegalese midfielder and the English defender duly obliged, delivering a merited victory over Marco Silva’s toothless side.

The Merseyside club's second win in nine matches was relatively comfortable as Fulham showed the reason their top marksman this season is goals gifted by opponents. Apart from a short spell in the second half, the away side were contained all match by Everton’s greater urgency and technical ability. The Blues had three goals ruled out for infringements, but a close-range strike from Gueye 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 one was more in need of scoring more than the young striker, the Everton forward who had gone 10 Premier League outings without a shot on target after his £27m summer arrival from the Spanish side and missed a gilt-edged chance to put his team 2-0 up at Sunderland earlier in the week. The 23-year-old headed the first opportunity of the game wide of the Fulham keeper's goal frame when picked out by Iliman Ndiaye’s excellent delivery.

Everton dominated the early exchanges and the Fulham goalkeeper pushed over James Garner’s long-range set-piece, awarded after Sasa Lukic was booked for hauling down Kiernan Dewsbury-Hall. Lukic tripped the same player again before halftime but the official, the man in charge, rightly ignored Everton appeals for a sending off. The Fulham boss was not risking anything, though, and withdrew the midfielder at the interval.

Barry thought his luck had finally turned when sliding in at the back post to convert a low cross by his teammate. But the joy of a maiden strike was erased by an assistant referee’s flag. The attacker was in an illegal position 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 continued in front of goal, but his overall display justified Moyes’ decision to keep the faith. His movement and work-rate kept busy the opposition's back line and contributed to the hosts the upper hand all game.

The Londoners grew into the game slowly with the Norwegian and the former Everton midfielder Alex Iwobi working well in midfield, but the first half threat from the visitors was minimal. The Mexican striker shot tamely at Jordon Pickford when teed up in the box by Iwobi and sent a free-kick from a promising location straight into the defensive barrier. That summed up their attacking output.

The Blues, inspired by Dewsbury-Hall and the forward, had a second goal chalked off for offside when Leno parried a Keane header and James Tarkowski volleyed in the loose ball. The skipper had moved beyond the last defender when heading on Jack Grealish’s cross in the build-up. But the team's third attempt beating the keeper counted. The left-back floated a perfect ball to the back post when left unmarked on the left flank by the youngster. Tarkowski met it with a powerful nod off the crossbar and, though the midfielder mishit the rebound, his teammate Gueye finished from point-blank. The relief inside the ground was evident.

The home side had a third goal ruled out early in the second half after the playmaker scored from a further excellent Mykolenko cross. Ndiaye had cushioned the delivery into Barry, who was in an offside position when competing with the Fulham defender for the touch that fell to the home player. Everton would have to wait until the 81st minute for the comfort of a two-goal lead. The provider was the architect with a corner that Keane glanced past Leno. He did so with the upper body, and Fulham’s appeals for handball were rejected by VAR.

Fulham carried more of a threat following the substitutions of Josh King, Rodrigo Muniz and the winger. The Everton keeper made a fine stop with his feet to prevent the substitute scoring with his initial involvement and denied the speedster with another important stop late on.