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 number of people diagnosed with the most dangerous form of skin cancer has almost tripled in 20 years, according to new figures.
A Welsh think tank says the progress made in reducing poverty in Wales is 'disappointing' and is calling on the Welsh government to do more.
All very average out there today! A mixture of sunshine and showers, with relatively decent temperatures!