Everton failed to pull clear of the danger zone as they suffered a 3-1 defeat against Fulham at Goodison Park on Saturday afternoon.
Harrison Reed and Dwight McNeil scored for either side to end the first half level before Harry Wilson and Daniel James grabbed their first league goals of the season to sink the hosts in the second half.
Having lost each of their last five matches, Fulham made the trip to Merseyside in search of a pick-me-up as they looked to keep their dreams of a place in Europe alive.
The Cottagers' current run of form saw their quest for a first FA Cup title come to an end on March 19 when they were beaten 3-1 by Manchester United in the quarter-finals.
As for Everton, they were looking to pull clear of the danger zone as they came into the weekend level on 27 points with 18th-placed Nottingham Forest and four above rock-bottom Southampton.
Sean Dyche's men came into the weekend off the back of a 2-0 defeat at the hands of Manchester United, a result which saw their four-game unbeaten run come to an end.
The loss at Old Trafford meant that Everton have managed just two wins in their last 32 Premier League away games and are winless in their last 11, claiming four draws and losing seven since October's 2-1 victory at Southampton.
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However, a solid home form had the Merseyside outfit optimistic coming into the weekend as they have picked up three wins and 10 points from their five games at Goodison Park since Dyche's appointment.
Following a cagey first 20 minutes, Fulham took the lead when Wilson's left-footed curler crashed off the post and into the path of Reed, who showed great composure in the follow-up to open the scoring.
This served as a wake-up call for the hosts, who fought back into the game and grabbed a much-reserved leveller five minutes after the hour mark courtesy of a low strike from McNeil.
James Garner wriggled his way through the Fulham midfield before releasing McNeil, whose first touch on the turn set the ball nicely for him to find the target from just outside the box.
The former Burnley man, who has started each of Everton's six games under Dyche's stewardship, is now the Toffees' top scorer in the league with four goals to his name.
Everton's continued pressure almost paid off five minutes later when Neal Maupay was set through on goal following a neat one-two with McNeil in the crowded Fulham box, but Bernd Leno made himself big enough to deny the French striker his first league goal since August.
McNeil was at it again on the stroke of half time, this time receiving the ball from Iwobi on the left and whipping in a dangerous cross into the Fulham box, but Demarai Gray could only steer his near-post volley wide of the post.
The second half kicked off with McNeil picking up from where he dropped off before the break as his cross caught Leno off-guard before bouncing off the frame of the post.
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However, Marco Silva's side took the lead thanks to a beautifully worked team goal in the 51st minute. Against the run of play, Tete found Willian at the far post with an inch-perfect cross, with the former Chelsea man cushioning the ball into the centre of the Fulham box for Wilson to tuck home his first league goal of the season.
It was all Fulham from there on, with Andreas Pereira, Willian and Joao Palhinha all having a go at Jordan Pickford before Daniel James struck in the 68th minute to silence the Goodison Park crowd.
James's pace and ability to run in behind put the Toffees to the sword as the former Manchester United forward latched on to Tete's teasing free kick to also open his Premier League account for Fulham.
With chances at a premium for Everton, Garner came close to pulling one back in the 89th minute but the former Manchester United midfielder saw his effort stray just inches wide of the Fulham post.
The Merseyside outfit have now failed to win any of their last four outings, losing twice and claiming two draws since their 1-0 victory over Brentford on March 11.
While Everton remain 17th in the league standings, a win or draw for Nottingham Forest in Sunday's game against Manchester United could see the Toffees slide into the bottom three.
As for Fulham, victory at Goodison Park means that they stand an outside chance of a place in Europe as they sit 10th in the table, eight points behind sixth-placed Aston Villa.
