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David Moyes had made clear before Fulham's visit that the onus for scoring goals should not rest only on his side's strikers. “I want more goals from my centre-halves and midfielders as well,” he declared. The Senegalese midfielder and the English defender responded perfectly, securing a well-earned victory over the opposition's toothless side.

Everton’s second win in nine matches was fairly straightforward as the visitors highlighted why their top marksman this season is opposition own goals. Aside from a short spell in the latter period, the visitors were kept quiet all match by Everton’s greater urgency 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 Keane’s late conversion made sure 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 gone 10 Premier League outings without testing the goalkeeper after his £27m summer arrival from Villarreal and missed a gilt-edged chance to put his team 2-0 up at the Stadium of Light on Monday. The 23-year-old headed the first opportunity of the game over Bernd Leno’s crossbar when found by his teammate'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 yellow-carded for hauling down Kiernan Dewsbury-Hall. Lukic tripped the same player later in the half but the official, the man in charge, correctly waved away home protests for a sending off. Silva was not risking anything, though, and substituted the midfielder at the break.

Barry thought his luck had finally turned when arriving at the back post to turn in a low cross by his teammate. But the joy of a first Everton goal was wiped out by an linesman's decision. Ndiaye was offside when attacking the delivery, and failing to connect, and the video assistant referee supported the original call. Barry’s misfortune may have persisted in the final third, but his all-round performance validated Moyes’ decision to keep the faith. His runs and work-rate kept busy the opposition's back line and helped give the hosts the edge all game.

The Londoners came into the contest 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 minimal. Raúl Jiménez fired weakly at the England keeper when set up inside the area by Iwobi and put a set-piece from a dangerous position directly at the Everton wall. That summed up their attacking output.

The Blues, inspired by Dewsbury-Hall and the forward, had a second goal chalked off for an infringement when the Fulham goalkeeper saved a effort from Keane and the captain fired home the rebound. The skipper had moved beyond the last defender when nodding down the winger's cross in the buildup. But Everton’s third attempt beating the keeper did stand. The left-back floated a lovely cross to the back post when found in space on the left by the youngster. Tarkowski connected with a thumping header off the crossbar and, though Iroegbunam mishit the rebound, his midfield partner the scorer converted from close range. The sense of release inside Hill Dickinson Stadium was evident.

The home side had a third goal disallowed early in the second half after the playmaker scored from a further excellent delivery from the left. Ndiaye had cushioned the delivery into the striker, who was offside when competing with Joachim Anderson for the ball that reached the Everton midfielder. Everton would have to wait until the 81st minute for the security of a second goal. The provider 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 a handball were rejected by VAR.

Silva’s side posed more danger following the introductions of Josh King, Rodrigo Muniz and the winger. The Everton keeper saved well with his legs to deny Muniz scoring with his initial involvement and denied Traoré with another important stop in the dying moments.