On-loan striker Josh Maja scored twice on his full Premier League debut as Fulham recorded a first ever league win at Everton with a deserved 2-0 victory ending a 12-match run without a win.
The 22-year-old Bordeaux loanee scored two typical poacher's goals from close range to move the third-bottom Cottagers to within seven points of Newcastle in 17th. The results offered them some hope of an escape if Maja can reproduce this form on a more regular basis.
They will not find many opponents as passive as Everton, however, who blew the chance to strike a psychological blow for the forthcoming Merseyside derby.
Four points from this match and Manchester City on Wednesday would have put them above their rivals across Stanley Park ahead of Saturday's short trip to Anfield, but Everton were toothless without injured top scorer Dominic Calvert-Lewin and also lacked the necessary competitiveness to make Fulham's first league win at Goodison Park in 28 attempts anything other than comfortable.
Bobby Decordova-Reid's cheeky backheel from a corner looping over a crowded six-yard area and onto a post set the early tone and was followed by Harrison Reed driving just wide of the angle of post and crossbar.
Everton's best chance came from full-back Seamus Coleman, who ran unchallenged from the halfway line to strike a post with a left-footed shot from outside the area in the 34th minute.
Within five minutes of the restart Ola Aina burst forward from left-back to cross for the unmarked Maja to slide home his first Premier League goal on only his second appearance.
Coleman and midfielder Tom Davies made way for Michael Keane and Josh King as manager Carlo Ancelotti made his second formation switch of the game by going to 4-4-2.
After Maja made it 2-0 in the 65th minute, King was denied a debut goal by an offside flag but there was little else to trouble the visitors' defence as Everton slipped to a third home defeat in four matches.