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David Moyes had made clear before the match against Fulham that the responsibility for scoring goals must not fall solely on his side's strikers. “I expect more goals from my defenders and midfielders as well,” he declared. Idrissa Gueye and the English defender responded perfectly, earning a fully deserved victory over Marco Silva’s ineffective side.

The Merseyside club's second victory in nine outings was largely untroubled as Fulham showed the reason their top marksman this season is opposition own goals. Apart from a short spell in the latter period, the visitors were kept quiet throughout by the home team's greater urgency and technical ability. Moyes’ team had three efforts disallowed for infringements, but a close-range strike from Gueye in added time before the break and Keane’s second-half header made sure 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 forward who had gone 10 Premier League outings without testing the goalkeeper after his big-money move from Villarreal and missed a clear opportunity to put his team 2-0 up at Sunderland earlier in the week. The 23-year-old headed the first opportunity of the game over Bernd Leno’s goal frame when found by his teammate's excellent delivery.

Everton controlled the early exchanges and the visiting shot-stopper pushed over James Garner’s 30-yard free-kick, given after Sasa Lukic was yellow-carded for fouling the Everton midfielder. The Serbian tripped the same player later in the half but the official, the man in charge, rightly ignored home protests for a second yellow. Silva was not risking anything, though, and withdrew the player at the interval.

The striker thought his fortune had finally turned when arriving at the back 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 offside when going for Gueye’s cross, and failing to connect, and the video assistant referee backed up the original call. Barry’s misfortune may have continued in the final third, but his overall display justified the manager's choice to stick with him. His movement and work-rate occupied Fulham’s central defenders and helped give Everton the upper hand throughout.

The Londoners came into the contest slowly with the Norwegian and the former Everton midfielder Alex Iwobi working well in the engine room, but the first half threat from the away team was minimal. Raúl Jiménez fired weakly at the England keeper when teed up inside the area by his teammate and put a set-piece from a dangerous position straight into the Everton wall. And that was it.

Everton, inspired by Dewsbury-Hall and the forward, had a another strike chalked off for offside when Leno parried a effort from Keane and James Tarkowski fired home the loose ball. The home captain had moved beyond the last defender when nodding down Jack Grealish’s delivery in the build-up. But Everton’s third attempt past Leno counted. The left-back delivered a lovely cross to the back post when found in space on the left by the youngster. The defender met it with a thumping header off the crossbar and, though the midfielder mishit the rebound, his midfield partner Gueye converted from point-blank. The sense of release inside Hill Dickinson Stadium was palpable.

Everton had a third goal ruled out early in the second half after Dewsbury-Hall scored from another inviting Mykolenko cross. The attacker had cushioned the delivery into Barry, who was in an offside position when challenging Joachim Anderson for the touch that fell to the home player. The team would have to wait until the 81st minute for the security of a two-goal lead. The provider was the architect with a set-piece that Keane directed past Leno. He scored with the upper body, and the visitors' protests for a handball were rejected by the video official.

Silva’s side carried more of a threat following the substitutions of Josh King, the Brazilian and Adama Traoré. Pickford saved well with his legs to deny the substitute finding the net with his first touch and denied Traoré with a crucial save late on.