Second-half goals from Leighton Baines and Nikica Jelavic saw Everton leapfrog Swansea in the Barclays Premier League table and become just the third away side to win at the Liberty Stadium this season.
Baines dusted himself down after being fouled by Ashley Williams to curl a lovely free-kick beyond Michel Vorm just before the hour and Jelavic sealed the 2-0 win by tapping in his second goal for the Toffees with 14 minutes remaining.
Swansea had dominated possession during the opening half but could not make it pay as Gylfi Sigurdsson and Danny Graham failed to convert their best chances.
As with most visitors to the Liberty Stadium this season, Everton had to cope without the ball for long periods and Wayne Routledge blazed a presentable chance over after Joe Allen's cushioned lay-off, while Phil Jagielka bravely cleared a dangerous Sigurdsson cut-back seconds later.
Having soaked up so much first-half pressure, the Toffees grabbed the lead just before the hour as Baines stepped up to curl a left-footed free-kick into the right corner of the net after Williams had brought the England international down on the edge of the box.
As the hosts pressed forward they left themselves vulnerable to the counter and, after Steven Pienaar had curled an effort wide, the South African teed up Jelavic who fired horribly off target with just Vorm to beat. The former Rangers' striker then missed another fine chance as he failed to connect with Baines' cut-back, but he made no such mistake in the 76th minute when substitute Marouane Fellaini turned past Williams in the box to give the striker a tap in.