On-loan striker Josh Maja scored twice on his full Premier League debut as Fulham recorded a first league win at Everton in their history, ending a 12-match winless run.
The 22-year-old former Sunderland man scored two typical poacher's goals from close range.
It moved Fulham to within seven points of Newcastle in 17th and offered them some hope of an escape if Maja, whose two goals moved him to joint-fourth on Fulham's leading league scorers list this season, 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 huge 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 and former Everton winger Ademola Lookman somehow shooting wide having cut in from the left.
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.
By then Richarlison had taken the last of his four touches of the half as even a move to a more central role did not improve his fortunes.
While Fulham failed to take advantage of having the better of the opening 45 minutes they did not need long to rectify that after the break.
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.
The same combination almost added a second but for the outstretched foot of Mason Holgate and that prompted a change of personnel and formation.
Coleman and midfielder Tom Davies made way for Michael Keane – with Holgate moving to right-back – and Josh King as manager Carlo Ancelotti made his second formation switch of the game by going to 4-4-2.
After Bordeaux loanee Maja had 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.
It was also the first time Ancelotti had failed to win in four home league games since December 2007 and next up are the in-form City.