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 Pride of Britain Awards are less than a month away, and today we find out who'll represent Wales in the Fundraiser of the Year category.
Police are appealing for information following a sexual assault on a 29 year old woman that took place in Pontllanfraith.
The personal tragedies and triumphs that have shaped his life. Terry Yorath: Life on the Edge, ITV Cymru Wales on Monday, 23 October (8pm).