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David Moyes had stressed before Fulham's visit that the responsibility for finding the back of the net must not fall solely on the team's strikers. “I demand more goals from my centre-halves and central players as well,” he declared. Idrissa Gueye and the English defender duly obliged, securing a well-earned victory over the opposition's toothless side.

Everton’s second victory in nine outings was relatively comfortable as the visitors demonstrated the reason their top marksman this season is opposition own goals. Apart from a short spell in the second half, the away side were subdued all match by Everton’s superior intensity and technical ability. Moyes’ team had three goals disallowed for offside, but a close-range strike from Gueye in added time before the break and the defender's second-half header ensured there would be no reprieve for their ex-coach.

No one was more in need of scoring as much as Thierno Barry, the Goodison Park forward who had failed to register a shot on target in 10 league games without testing the goalkeeper after his £27m summer arrival from Villarreal and missed a clear opportunity to put his team two goals ahead at Sunderland earlier in the week. The youngster headed the first opportunity of the game over Bernd Leno’s crossbar when found by Iliman Ndiaye’s fine cross.

Everton controlled the early exchanges and the visiting shot-stopper pushed over James Garner’s long-range set-piece, given after Sasa Lukic was booked for hauling down the Everton midfielder. The Serbian brought down the same player later in the half but the referee, Andrew Madley, correctly waved away home protests for a second yellow. Silva was not risking anything, though, and substituted the midfielder at the interval.

The striker believed his luck had changed at last when arriving at the far post to turn in a drilled pass by Gueye. But the joy of a first Everton goal was erased by an assistant referee’s flag. Ndiaye was in an illegal position when going for the delivery, and missing, and the VAR supported the on-field decision. The forward's bad luck may have continued in the final third, but his overall display justified the manager's choice to keep the faith. His movement and work-rate kept busy the opposition's back line and contributed to the hosts the edge all game.

Fulham grew into the game slowly with the Norwegian and the former Everton midfielder Alex Iwobi working well in the engine room, but the first half threat from the visitors was minimal. The Mexican striker fired weakly at the England keeper when set up inside the area by his teammate and sent a set-piece from a dangerous position straight into the defensive barrier. That summed up their attacking output.

The Blues, driven on by Dewsbury-Hall and the forward, had a second goal disallowed for an infringement when Leno saved a Keane header and James Tarkowski fired home the rebound. The home captain had moved beyond the last defender when nodding down Jack Grealish’s delivery in the build-up. But Everton’s next effort past the keeper did stand. The left-back delivered a perfect ball to the back post when left unmarked on the left flank by the youngster. The defender met it with a powerful nod off the crossbar and, though the midfielder fluffed his lines, his teammate Gueye converted from close range. The relief inside Hill Dickinson Stadium was evident.

The home side had a third goal ruled out after the restart after Dewsbury-Hall found the bottom corner from another inviting delivery from the left. Ndiaye had laid off the delivery into Barry, who was in an offside position when challenging Joachim Anderson for the touch that fell to the Everton midfielder. Everton would have to be patient until the closing stages for the comfort of a second goal. Dewsbury-Hall was the creator with a corner that Keane glanced past the goalkeeper. He scored with the back of his shoulder, and Fulham’s appeals for a handball were rejected by the video official.

Fulham carried more of a threat after the substitutions of Josh King, the Brazilian and Adama Traoré. The Everton keeper made a fine stop with his feet to deny the substitute scoring with his initial involvement and stopped the speedster with another important stop late on.