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
In this today's Newsweek Wales, Carl talks about cancer survival rates in Wales and the search for volunteers to train guide dog puppies.
It'll be brighter today with some lingering blustery showers. This evening it'll be colder under clear skies, with isolated showers.
Gareth Bale put any domestic troubles behind him as he starred in Wales' emphatic 3-0 win over Israel in Haifa.