Fulham dented Everton's Champions League hopes with a comfortable win.
Collins John scored from close range after 15 minutes and former Everton striker Brian McBride's towering header added a second before the interval.
Everton, who lost Tim Cahill to injury early on, only had one clear-cut chance when Lee Carsley shot wide of an open goal early in the second-half.
Fulham had midfield man Papa Bouba Diop sent off for two yellow cards, but held on to assure Premiership survival.
Everton had the ball in the net inside the opening minute, but Kevin Kilbane strayed offside as he touched in David Weir's header.
And Everton suffered another setback after 12 minutes when the lost influential midfield Cahill, who injured his back after being tackled by Diop.
Fulham's attack was causing early problems for the Everton defence, and they took the lead after 15 minutes, when John took advantage of a deflection to lash a comprehensive finish past Nigel Martyn from 15 yards.
Everton could not establish any measure of control, their only threat coming when Duncan Ferguson's header from Alessandro Pistone's cross was clutched low down by Edwin van der Sar.
And Fulham doubled their lead six minutes before the interval, when McBride rose superbly to power Luis Boa Morte's header past Martyn.
Lee Carsley wasted a glaring opportunity to pull a goal back for Everton after 47 minutes, but he somehow failed to hit the target from close range after Ferguson nodded into his path.
Everton were failing to make any impact and boss Moyes made a double change after 63 minutes, sending on James Beattie and James McFadden for Mikel Arteta and Marcus Bent.
Fulham were reduced to 10 men with 15 minutes left when Diop, who had earlier been booked, was sent off for draggintg back McFadden.
Everton posed a rare threat to the Fulham goal when Ferguson's header flashed across the face of goal with Carsley unable to provide the final touch.
Fulham boss Chris Coleman:
"It was good to see players show a bit of character they have sometimes lacked this season.
"We've lacked consistency and too many players have been inconsistent but I know the direction I want to go in.
"The players just have to realise they must roll up their sleeves and go to war if they play for Fulham."
Everton boss David Moyes:
"We've had some good ones this season but this wasn't one of them. We didn't play well.
"We've done well to qualify for the UEFA Cup, but I would be silly to talk about the fourth place being taken away from us when we haven't achieved it.
"We need to get the form back which beat Manchester United."
Fulham: Van der Sar, Volz, Knight, Goma, Rosenior,
Radzinski (Jensen 63), Diop, Clark, Boa Morte, McBride,
John (Cole 61).
Subs Not Used: Bocanegra, Pembridge, Crossley.
Sent Off: Diop (76).
Goals: John 15, McBride 39.
Everton: Martyn, Watson, Weir, Yobo, Pistone,
Bent (Beattie 64), Arteta (McFadden 64), Cahill (Osman 13),
Carsley, Kilbane, Ferguson.
Subs Not Used: Plessis, Wright.
Booked: Pistone, Arteta, McFadden.
Ref: S Bennett (Kent).