Everton became only the second club to complete a Premier League double over the Swans as goals from Leighton Baines and Nikica Jelavic sealed victory for the visitors.
Baines curled a sublime free-kick into the top corner for the opener after 59 minutes before Jelavic side-footed home with 14 minutes left.
It meant Everton joined Norwich in completing the double over the Swans, who dropped two places to tenth after this defeat.
The Swans made just one change to the starting XI that won at Fulham.
Brendan brought Ashley Williams back into the side after the Wales international missed out at Craven Cottage due to a virus. That meant Garry Monk steps down to the bench after helping the club to a third successive victory - and clean sheet - in the Premier League.
The Swans started the day in eighth - two points ahead of Everton and just three behind seventh-placed Liverpool.
Everton included Darron Gibson in their starting XI after he came through a fitness test while Tim Cahill got the nod to play in behind Nikica Jelavic, with Marouane Fellaini among the substitutes.
Swans: Michel Vorm, Angel Rangel, Steven Caulker, Ashley Williams (capt), Neil Taylor, Leon Britton, Joe Allen, Gylfi Sigurdsson, Wayne Routledge (Leroy Lita, 72), Scott Sinclair (Josh McEachran, 72), Danny Graham (Luke Moore, 72).
Subs: Gerhard Tremmel, Garry Monk, Alan Tate, Josh McEachran, Mark Gower, Luke Moore, Leroy Lita.
Everton: Tim Howard, Tony Hibbert, Leighton Baines, Darron Gibson (John Heitinga, 84), Phil Jagielka, Nikica Jelavic (Denis Stracqualursi, 82), Sylvain Distin, Tim Cahill (Marouane Fellaini, 58), Phil Neville (capt), Leon Osman, Steven Pienaar.
Subs: Jan Mucha, James McFadden, Magaye Gueye, Victor Anichebe.
In perfect conditions at the Liberty, the Swans signalled their intent in the early stages.
Angel Rangel's superb through ball put Danny Graham in on goal with Sylvain Distin left stranded, but the striker opted against squaring for Scott Sinclair and then saw his shot parried and collected by Tim Howard.
Graham played a part in the next attack, flicking on Neil Taylor's curling cross which bounced along the face of goal and then out of danger.
The Swans kept probing away, Taylor robbing Leon Osman of possession 25 yards out before teeing up Gylfi Sigurdsson, but his shot dragged wide.
Another attack followed, Taylor's cross being touched down by Sigurdsson for Wayne Routedge, but his shot was high and wide.
Sigurdsson was involved in the next move, pinching loose ball after some sloppy defending from the visitors before seeing his low drive cleared for a corner by Phil Jagielka. From the corner, Everton could only clear as far as Joe Allen outside the box, but his powerful shot went well wide.
With 27 minutes on the clock David Moyes's side created their first attack with Nikica Jelavic heading wide from a free-kick.
It proved a brief respite for the visitors as the Swans continued to push on. This time a fine through ball from Routledge found Sigurdsson, but his shot deflected off Jagielka for a corner.
With just one minute of added on time signalled, the Swans pushed hard to find an opener before the break as Steven Caulker threaded through a fine pass for Rangel, whose low cross for Graham was cut out again by the solid Jagielka.
Half-time: Swans 0 Everton
The Swans survived a scary moment just 60 seconds into the half as Ashley Williams's attempted clearance deflected off Osman and dropped to Jelavic, but the striker - under pressure from Taylor - directed his effort high and wide.
Almost immediately the Swans forced Everton into conceding possession, which saw Sigurdsson race on before his shot cannoned off Jagielka and out for a corner.
Everton replied through Darron Gibson, who forced a good save from Michel Vorm after his trademark left-footed shot looked goalbound. Jelavic latched onto the loose, but his shot-come-cross just failed to find the onrushing Cahill.
Graham then nodded over from Routledge's cross as the game continued to excite heading towards the hour mark.
Steven Pienaar then fired wide for the visitors before Sinclair cut inside and saw his effort fail to trouble Howard.
But the visitors found the opener. After Leighton Baines had been fouled 20 yards out, he dusted himself off to curl a delightful free-kick into the top right-hand corner.
Pienaar went close to doubling the lead as following a neat counter and through ball from Gibson, the South African curled his effort just past the post.
With the Swans failing to find a way through the Everton defence, Brendan made a triple substitution with Josh McEachran, Luke Moore and Leroy Lita coming on in place of Sinclair, Graham and Routledge for the remaining 18 minutes.
But it was the visitors who carved open the next chance - a great one at that - as sub Marouane Fellaini pinched dispossessed Allen and found Jelavic via Pienaar. But the former Rangers striker pushed his shot wide when well placed.
The lead was doubled soon after though as Fellaini shrugged off Williams and cut back for Jelavic, who side-footed into the far corner with a neat finish.
Lita then fired wide before Vorm did well to deny sub Denis Stracqualursi as the game entered the final few minutes.
Despite four minutes of added on time, the Swans couldn't find a consolation against a stern Everton backline.