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David Moyes had stressed before Fulham's visit that the responsibility for scoring goals must not fall solely on his side's strikers. “I demand more goals from my defenders and central players as well,” he declared. The Senegalese midfielder and Michael Keane duly obliged, earning a fully deserved victory over the opposition's toothless team.

The Merseyside club's second victory in nine matches was largely untroubled as Fulham showed the reason their leading scorer this season is goals gifted by opponents. Aside from a short spell in the latter period, the away side were subdued all match by the home team's superior intensity and quality. Moyes’ team had three efforts disallowed for offside, but a poacher’s finish from the midfielder in added time before the break and the defender's second-half header ensured there would be no comeback for the former Everton manager.

No one was more in need of scoring as much as Thierno Barry, the Everton attacker 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 on Monday. The 23-year-old directed the first opportunity of the game over the Fulham keeper's goal frame when picked out by his teammate's excellent delivery.

Everton dominated the opening stages and the Fulham goalkeeper pushed over the midfielder's 30-yard free-kick, given after the Fulham player was yellow-carded for hauling down Kiernan Dewsbury-Hall. The Serbian brought down the identical opponent again before halftime but the referee, Andrew Madley, correctly waved away Everton appeals for a second yellow. The Fulham boss was taking no further chances, however, and withdrew the player at the interval.

Barry believed his fortune had changed at last when arriving at the far post to turn in a low cross by his teammate. But the elation of a maiden strike was erased by an assistant referee’s flag. Ndiaye was offside when going for the delivery, and failing to connect, 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 Moyes’ decision to stick with him. His movement and work-rate kept busy the opposition's back line and contributed to Everton the upper hand throughout.

Fulham grew into the game slowly with the Norwegian and the former Everton midfielder Alex Iwobi combining effectively in the engine room, but the early danger from the visitors was minimal. Raúl Jiménez shot tamely at the England keeper when set up in the box by Iwobi and put a free-kick from a dangerous position straight into the defensive barrier. That summed up their attacking output.

The Blues, driven on by the midfielder and Ndiaye, had a another strike chalked off for offside when the Fulham goalkeeper parried a Keane header and the captain volleyed in the loose ball. The skipper had just strayed beyond the last defender when nodding down the winger's delivery in the buildup. But the team's next effort beating the keeper counted. Vitalii Mykolenko delivered a lovely cross to the back post when left unmarked on the left by the youngster. Tarkowski met it with a powerful nod against the bar and, though Iroegbunam mishit the rebound, his midfield partner the scorer finished from point-blank. The relief inside Hill Dickinson Stadium was evident.

Everton had a further effort disallowed early in the second half after Dewsbury-Hall scored from a further excellent Mykolenko cross. The attacker had cushioned the delivery into Barry, who was offside when competing with the Fulham defender for the touch that reached the Everton midfielder. Everton would have to wait until the closing stages for the security of a two-goal lead. Dewsbury-Hall was the architect with a set-piece that Keane glanced over 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, Rodrigo Muniz and the winger. Pickford saved well with his feet to deny the substitute scoring with his first touch and denied Traoré with another important stop late on.