A first half goal from Wilfried Bony and another on the 90th minute from Ashley Williams were not enough for Swansea City as their second trip to Goodison Park this season ended in defeat.
Garry Monk's men were knocked out of the FA Cup at the same venue last month and it was Everton who once again took the win.
Bony's first half goal put the Swans back into contention after Leighton Baines put the home side ahead with a penalty in the 20th minute.
But second half goals from Romelu Lukaku and Ross Barkley sealed the win for Roberto Martinez's team, before Williams secured a consolation goal for the Welsh side.
More top news
The last confirmed sighting of the 14-year-old was in Flint on Friday morning.
After a mostly dry evening with a few scattered showers, cloud and outbreaks of showery rain will spread northeast through the night.
Tributes have been paid to former Wales international Mel Charles, who has died at the age of 81.