The Swans were held to a goalless draw by Everton in a tight and fiercely-contested clash at the Liberty Stadium.
The visitors shaded the first half with Steven Naismith going close, while Bafe Gomis shot wide when he raced clear of the Everton defence.
Both sides had their moments in the second period, Romelu Lukaku blazing over the bar from inside the box and Jefferson Montero drawing a fine stop from Tim Howard at the other end.
Everton ended the game with ten men as substitute Kevin Mirallas was shown a straight red card for a challenge on Modou Barrow in stoppage time, as both sides settled a share of the spoils.
The Swans made one change to the starting line-up as Jefferson Montero started in place of Wayne Routledge after coming off the bench in last week's defeat at Watford.
On the bench, Ki Sung-Yueng was included after returning from South Korea following the birth of his daughter.
Everton were without Seamus Coleman and Muhamed Besic after they sustained injuries in the win over Chelsea, while Bryan Oviedo was also ruled out with a knee injury.
Tyias Browning and Steven Naismith - who scored a hat-trick against the Blues - were handed starts by boss Roberto Martinez.
Lukasz Fabianski, Kyle Naughton, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Jack Cork, Jonjo Shelvey, Gylfi Sigurdsson (Ki Sung-Yueng, 60), Jefferson Montero, Andre Ayew (Modou Barrow, 87), Bafe Gomis (Eder, 81).
Kristoffer Nordfeldt, Angel Rangel, Kyle Bartley, Wayne Routledge.
Tim Howard, John Stones, Phil Jagielka (capt), Arouna Kone (Gerard Deulofeu, 65), Romelu Lukaku, Steven Naismith, James McCarthy, Gareth Barry, Ross Barkley (Kevin Mirallas, 90), Tyias Browning, Brendan Galloway.
Joel Robles, Darron Gibson, Aaron Lennon, Leon Osman, Ramiro Funes Mori.
The game saw a number of chances in the opening 20 minutes, with Everton enjoying the early attempts.
After a brief halt for clash of heads between Andre Ayew and Phil Jagielka, the visitors saw Romelu Lukaku's 20-yard free-kick bravely diverted wide for a corner by Ashley Williams, before the Everton captain headed over Ross Barkley's resulting delivery.
The Swans took time to get going, but Bafe Gomis' acrobatic effort from a Kyle Naughton cross before the striker latched onto Gareth Barry's header before racing in on goal. Gomis, though, scuffed his effort wide from 15 yards.
At the other end, a fine Everton counter saw Arouna Kone find Lukaku, and when he teed up Steven Naismith the Scot was only denied by Neil Taylor's sliding challenge.
Naismith was at it again soon after, with his shot deflected by Lukaku some ten yards out, but Lukasz Fabianski did well to get down low to gather cleanly.
The game continued to flow end to end, and the final chance of the half saw Jefferson Montero cross to Gomis, but his effort was blocked out.
HALF-TIME: Swans 0 Everton 0
The game continued much like the first half, with both chances getting opportunities to open the scoring.
Ayew headed wide from a Montero cross while, at the other end, Gomis had to be alert to clear a Barkley cross after it had deflected off Williams.
Everton left-back Brendan Galloway then had a good opportunity after turning in the box, but he scuffed his angled effort wide.
Lukaku had an even better chance after latching onto Gareth Barry's fine through ball, but he lacked composure and drilled high and wide from just inside the area.
The Swans then saw Gylfi Sigurdsson's free-kick brush the sidenetting, but the visitors again went close as Williams cleared Lukaku's effort off his own line.
The Swans made their first sub as Ki Sung-Yueng replaced Sigurdsson on the hour, and within a minute of that Montero beat his man before seeing his thunderous shot tipped over by Tim Howard.
Then Gomis tested Howard as his powerful effort flew straight at the American, who swatted it aside and away from danger.
Everton then probed, with a cross from sub Gerard Deulofeu flying along the face of goal and then Galloway saw his goal-bound effort header over by skipper Williams.
The tension levels rose at the Liberty as Barkley's chipped pass sent Lukaku in on goal, but a brave and well-timed sliding challenge from Taylor denied the striker.
Garry Monk then sent Eder and Modou Barrow on for Gomis and Ayew as the game entered the final moments.
There was more controversy in added-on time as Everton sub Kevin Mirallas was dismissed for a lunge on fellow replacement Barrow.
And, after Ki skied a late effort, the whistle was blown on an entertaining 0-0 draw with both sides deservedly sharing the spoils.