Goals from Bobby Decordova-Reid and substitute Ruben Loftus-Cheek were not enough to pull Fulham further away from the Premier League relegation zone, as Ivan Cavaleiro became the latest player to miss a penalty.
It took less than a minute for the Whites to concede when Bobby Decordova-Reid’s loose touch fell to Richarlison, whose square ball bounced in off Dominic Calvert-Lewin from close range.
They settled quickly soon after though, and were level within 15 minutes. Decordova-Reid – who started alongside Cavaleiro in place of the benched Aleksandar Mitrović – first scuffed an effort that should have tested Jordan Pickford.
And the Jamaica international immediately made amends with his fourth goal of the season, slotting into the far corner off a neat one-two exchange from Tom Cairney.
But Everton’s fluid front three caused problems throughout the first period, with several careless mistakes in and out of possession also hampering the home side.
An effervescent Richarlison, back from a three-match ban, pounced to force a save from Alphonse Areola low to his left, and the Toffees eventually regained their lead on the half-hour mark when Calvert-Lewin fired in first time from a Lucas Digne delivery.
Digne, who enjoyed plenty of space each time he received the ball in the left channel, then crossed perfectly again onto the head of Abdoulaye Doucouré to give the visitors a two-goal cushion going into the break.
Mitrović and Loftus-Cheek were sent on soon after the restart as the Whites looked to mount their comeback, and the pair combined beautifully to draw a foul in the box from Ben Godfrey before Cavaleiro slipped and botched his spot-kick over the bar.
However the Whites responded straightaway when Loftus-Cheek notched his first goal for the club, powering home Ademola Lookman’s pull-back via a deflection to give Fulham hope in the final 20 minutes.
They pinned Everton back with desperate attempts to break their resolute defensive banks, but their first-half sloppiness ultimately proved costly.
Fulham: Areola, Aina, Andersen, Adarabioyo, Robinson, Reed, Lemina (Anguissa 69), Cairney (Loftus-Cheek 58), Cavaleiro, Lookman, Decordova-Reid (Mitrović 58)