Idrissa Gueye and Michael Keane find the net as Everton overcome the Cottagers

David Moyes had stressed before the match against Fulham that the onus for finding the back of the net should not fall solely on his side's forwards. “I demand more goals from my centre-halves and central players as well,” he stated. The Senegalese midfielder and the English defender duly obliged, securing a fully deserved victory over the opposition's toothless side.

The Merseyside club's second win in nine outings was fairly straightforward as the visitors demonstrated the reason their leading scorer this season is goals gifted by opponents. Apart from a brief flurry in the second half, the away side were kept quiet all match by Everton’s superior intensity and quality. Moyes’ team had three efforts ruled out for offside, but a close-range strike from Gueye in first-half stoppage time and the defender's second-half header ensured there would be no reprieve for the former Everton manager.

No player needed a goal as much as the young striker, the Goodison Park 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 the Spanish side and spurned a gilt-edged chance to put his team two goals ahead at Sunderland on Monday. The youngster headed the earliest chance of the game wide of Bernd Leno’s goal frame when found by Iliman Ndiaye’s fine cross.

Everton dominated the early exchanges and the visiting shot-stopper pushed over James Garner’s long-range set-piece, awarded after Sasa Lukic was booked for hauling down Kiernan Dewsbury-Hall. Lukic brought down the same player again before halftime but the referee, the man in charge, correctly waved away home protests for a second yellow. The Fulham boss was taking no further chances, however, and substituted the midfielder at the interval.

Barry believed his fortune had finally turned when sliding in at the back post to convert a drilled pass by Gueye. But the elation of a maiden strike was erased by an assistant referee’s flag. The attacker was offside when going for Gueye’s cross, and failing to connect, and the video assistant referee supported the on-field decision. Barry’s misfortune may have continued in the final third, but his all-round performance validated Moyes’ decision to stick with him. His runs and effort kept busy Fulham’s central defenders and helped give the hosts the edge throughout.

Fulham grew into the game gradually with the Norwegian and the former Everton midfielder Alex Iwobi combining effectively in the engine room, but the first half threat from the away team was limited. Raúl Jiménez fired weakly at Jordon Pickford when set up inside the area by his teammate and put a free-kick from a promising location straight into the Everton wall. That summed up their attacking output.

The Blues, driven on by Dewsbury-Hall and Ndiaye, had a second goal disallowed for an infringement when the Fulham goalkeeper saved a Keane header and the captain fired home the rebound. The skipper had moved offside when nodding down Jack Grealish’s cross in the buildup. But the team's third attempt beating Leno counted. The left-back floated a perfect ball to the back post when found in space on the left by Tim Iroegbunam. The defender connected with a powerful nod against the bar and, though Iroegbunam mishit the rebound, his teammate Gueye finished from point-blank. The relief inside Hill Dickinson Stadium was evident.

Everton had a further effort ruled out after the restart after the playmaker found the bottom corner from a further excellent delivery from the left. Ndiaye had laid off the delivery into the striker, who was offside when challenging Joachim Anderson for the touch that reached the Everton midfielder. Everton would have to be patient until the 81st minute 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 upper body, and the visitors' protests for handball were rejected by the video official.

Silva’s side posed more danger after the substitutions of the forward, Rodrigo Muniz and Adama Traoré. The Everton keeper made a fine stop with his legs to deny the substitute finding the net with his initial involvement and denied Traoré with a crucial save in the dying moments.