Idrissa Gueye along with Keane on target as the Toffees sink the Cottagers

The Everton manager had stressed before Fulham's visit that the responsibility for finding the back of the net must not fall solely on his side's forwards. “I demand more goals from my defenders and midfielders as well,” he insisted. The Senegalese midfielder and Michael Keane responded perfectly, delivering a well-earned victory over Marco Silva’s ineffective side.

The Merseyside club's second win in nine matches was largely untroubled as the visitors showed why their leading scorer this season is goals gifted by opponents. Aside from a short spell in the second half, the visitors were contained throughout by Everton’s superior intensity and quality. The Blues had three efforts disallowed for offside, but a poacher’s finish from Gueye in first-half stoppage time and the defender's late conversion made sure there would be no comeback for the former Everton manager.

No one needed a goal as much as Thierno Barry, the Everton attacker who had failed to register a shot on target in 10 league games without a shot on target after his £27m summer arrival from Villarreal 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 Bernd Leno’s crossbar when picked out by his teammate's fine cross.

The home side dominated the opening stages and the Fulham goalkeeper tipped over James Garner’s 30-yard free-kick, awarded after the Fulham player was booked for hauling down the Everton midfielder. Lukic brought down the same player later in the half but the referee, the man in charge, rightly ignored home protests for a second yellow. Silva was taking no further chances, though, and substituted the player at the break.

The striker thought his luck had finally turned when sliding in at the back post to convert a drilled pass by his teammate. But the elation of a maiden strike was wiped out by an assistant referee’s flag. Ndiaye was in an illegal position when going for Gueye’s cross, and missing, and the video assistant referee backed up the on-field decision. Barry’s misfortune may have continued in front of goal, but his overall display validated Moyes’ decision to keep the faith. His runs and work-rate occupied the opposition's back line and contributed to the hosts the edge throughout.

Fulham grew into the game slowly with the Norwegian and the former Everton midfielder Alex Iwobi working well in midfield, but the early danger from the visitors was limited. Raúl Jiménez fired weakly at Jordon Pickford when set up in the box by Iwobi and sent a free-kick from a promising location straight into the Everton wall. And that was it.

Everton, driven on by Dewsbury-Hall and Ndiaye, had a second goal chalked off for an infringement when the Fulham goalkeeper parried a effort from Keane and the captain volleyed in the rebound. The home captain had moved beyond the last defender when heading on the winger's cross in the build-up. But the team's third attempt beating Leno counted. Vitalii Mykolenko delivered a lovely cross to the far post when found in space on the left by Tim Iroegbunam. The defender met it with a thumping header off the crossbar and, though Iroegbunam fluffed his lines, his midfield partner the scorer finished from close range. The relief inside Hill Dickinson Stadium was evident.

The home side had a further effort disallowed early in the second half after Dewsbury-Hall found the bottom corner from a further excellent Mykolenko cross. Ndiaye had cushioned the delivery into Barry, who was in an offside position when competing with Joachim Anderson for the ball that reached the Everton midfielder. The team would have to wait until the closing stages for the security of a second goal. Dewsbury-Hall was the architect with a corner that the defender directed past Leno. He scored with the back of his shoulder, and Fulham’s appeals for handball were rejected by the video official.

Silva’s side carried more of a threat following the substitutions of the forward, Rodrigo Muniz and Adama Traoré. Pickford made a fine stop with his legs to prevent Muniz finding the net with his initial involvement and stopped the speedster with a crucial save in the dying moments.