The Toffees bounced back from their Merseyside derby loss to Liverpool by overpowering the previously in-form Swans who had won three on the trot prior.
Leighton Baines gave the visitors the lead just prior to the hour-mark with a brilliantly taken free-kick after he had been brought down by Ashley Williams on the edge of the area.
Swansea, as usual, were dominating possession but it fell to ill-effect when Everton went two ahead thanks to Nikica Jelavic's second goal for the club which came in the 76th minute. The Croatian got free in the area to easily slot home substitute Marouane Fellaini's low cross to allow his side to move up to ninth on the Premier League table.
Liberty Stadium, Swansea - 20,509