Victor Anichebe opened the scores for Everton
Everton ended Swansea City's unbeaten home record with a dominant display of power and precision in south Wales.
Victor Anichebe gave Everton a controversial opener when he volleyed home after a suspicion of handball from Marouane Fellaini in the build-up.
Kevin Mirallas finished a sweeping move on the second attempt to double the lead in a one-sided first half.
Swansea defender, Angel Rangel missed an open goal before Fellaini headed a third after Nathan Dyer's red card.