Leon Osman's header proved the difference as the Swans went down to a 1-0 defeat at Everton.
The midfielder leapt highest to meet Royston Drenthe's header on the hour as the Swans failed to make it back-to-back away cleansheets following the 0-0 draw at Newcastle last time out.
Danny Graham had the visitors' best chance, but he could only head straight at Tim Howard.
The Swans stuck to the same starting XI that earned a draw at Newcastle. Angel Rangel made a return to the bench after recovering from his ankle injury sooner than expected, while Nathan Dyer wasn't included in the matchday squad following a foot problem.
Everton: Tim Howard, Tony Hibbert, John Heitinga, Phil Jagielka, Leighton Baines, Seamus Coleman (Magaye Gueye, 31), Maraoune Fellaini, Phil Neville (capt), Leon Osman, Royston Drenthe (Tim Cahill, 80), Louis Saha (Denis Stracqualursi, 75). Subs: Jan Mucha, Sylvain Distin, Ross Barkley, James McFadden.
Swans: Michel Vorm, Jazz Richards, Steven Caulker, Ashley Williams (capt), Neil Taylor (Angel Rangel, 45+1), Leon Britton (Leroy Lita, 74), Mark Gower (Kemy Agustien, ht), Joe Allen, Wayne Routledge, Danny Graham, Scott Sinclair. Subs: Gerhard Tremmel, Garry Monk, Stephen Dobbie, Luke Moore.
Referee: Kevin Friend (Leicestershire)
The Swans settled into the encounter in the opening exchanges, and when a well-worked corner found its way to Scott Sinclair just off the penalty spot, the winger looked to have a decent opportunity. Although his first touch was too strong, Sinclair found Wayne Routledge, who fired in a low bouncing cross but keeper Tim Howard collected.
The first period had reached the halfway stage without any real danger of opening the scoring, but the Swans were happy with their work so far.
Everton's biggest moment of the game came when the lively Royston Drenthe jinked his way into the box and fed Leon Osman, who sent in a dangerous cross that Neil Taylor cleared only to see the offside flag raised.
John Heitinga then headed over Phil Neville's cross in the first effort of the half after 28 minutes before Drenthe's low centre was neatly disposed of by Steven Caulker.
David Moyes was then forced into a change as Magaye Gueye replaced the injured Seamus Coleman just after the half-hour mark.
The hosts were forcing themselves into the game more and more, with Drenthe's fine cross met by the head of Louis Saha, but the striker's effort bounced just wide of the far post.
The big chance for the hosts came in the 38th minute, Leighton Baines's cross finding sub Gueye. His shot was kept out by an outstanding save low down by Michel Vorm, and sub Gueye followed up with the rebound only to see it deflect off the arm of Ashley Williams and cleared for a corner.
The home crowd saw their appeals for a handball turned down, but just seconds later saw referee Kevin Friend penalise Williams for blocking Osman's effort with his arm. The centre-back was booked for his troubles, but Baines fired his free-kick from 20 yards high and wide.
The Swans were having to deal with a large period of pressure before the break, with Drenthe's curling free-kick from just outside the angle of the box whistling past the far post.
Just before the half-time whistle. Brendan was also forced into a change as Neil Taylor - injured during Gueye's big chance - was replaced by the returning Angel Rangel.
Half-time: Everton 0 Swans 0
Like at Newcastle last weekend, a change was made during the interval with Kemy Agustien again coming on in place of Mark Gower.
The half started slowly. with the Swans soaking up most of the early pressure. Osman found himself with a half chance after Neville's quickly-taken free-kick, but the midfielder's tame effort was easily collected by Vorm.
But then, on the hour, the hosts got their goal. Drenthe's inswinging corner found Osman, who headed neatly past Vorm.
Phil Jagielka then prodded another Drenthe corner just wide before the Swans had their best chance of the game. Allen found Routledge out on the right and the winger's cross was met by the head of Graham, who could only direct his effort straight at Howard.
Brendan then made his final change with 16 minutes left as Leroy Lita replaced Leon Britton while Everton also put Denis Stracqualursi on for Saha and Tim Cahill for Drenthe, who had been well marked all game by Jazz Richards.
But there was to be no dramatic comeback from the Swans, as they went down to a sixth defeat of the season.