The Swans bravely held on to claim a point at Everton despite Jonjo Shelvey's second-half dismissal.
Garry Monk's side were forced to battle on for the last 18 minutes with a man disadvantage as Shelvey was shown a second yellow card following a foul on James McCarthy.
But it was a deserved point for the Swans, with this 0-0 score proving their fifth clean sheet in ten Barclays Premier League matches.
This draw moved them onto 15 points from ten matches.
The Swans made four changes to their starting XI. From the Capital One Cup defeat to Liverpool in midweek, Lukasz Fabianski returned in goal while Gylfi Sigurdsson and Ki Sung-Yueng overcome injuries to return to action.
The final change saw Wilfried Bony lead the line up front while centre-back Federico Fernandez was available again after his red card at Liverpool was overturned following the club's appeal.
Tim Howard, Seamus Coleman, Phil Jagielka (capt), Antolin Alcaraz (Muhamed Besic, 32), Leighton Baines, Aiden McGeady (Romelu Lukaku, 68), Gareth Barry, Ross Barkley, James McCarthy, Steven Naismith (Steven Pienaar, 68), Samuel Eto'o.
Joel Robles, Tony Hibbert, Christian Atsu, Leon Osman.
Lukasz Fabianski, Angel Rangel, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Ki Sung-Yueng, Jonjo Shelvey, Gylfi Sigurdsson (Tom Carroll, 75), Wayne Routledge, Jefferson Montero (Nathan Dyer, 79), Wilfried Bony (Bafe Gomis, 60).
Gerhard Tremmel, Liam Shephard, Kyle Bartley, Marvin Emnes.
There was a lively start at Goodison Park with both sides going for goal in the opening exchanges.
Samuel Eto'o saw his effort easily collected by Lukasz Fabianski while Wilfried Bony's powerful shot was blocked out by Everton skipper Phil Jagielka.
Then, in what was a great opportunity to break the deadlock, Bony found himself in space and in on goal after Gylfi Sigurdsson's through ball caught out the home defence, but he took his time before guiding his low effort inches wide.
At the other end, Leighton Baines curled a 20-yard free-kick wide after Ki Sung-Yueng brought Eto'o's surging run to a sudden halt before Jonjo Shelvey's deflected effort was collected by Tim Howard with referee Kevin Friend waving away appeals of handball against Alcaraz.
That proved Alcaraz's final act as he was replaced by Muhamed Besic just past the half hour after he came off with a shoulder injury.
Jagielka flashed his header wide from a McGeady corner as Everton pressed for an opener in the closing stages, but both sides went into the break on level terms.
HALF-TIME: Everton 0 Swans 0
The Swans started the second half on the attack and Routledge almost caught out Gareth Barry as he looked to guide a loose ball to Howard, but the England international did enough to avert the danger.
Shelvey then steered a 20-yard effort wide after some sublime control and pass from Bony sent the midfielder hurtling towards goal.
That was Bony's final say as the striker, who had been booked in the first half, was replaced on the hour by Bafe Gomis.
At the other end, an Ashley Williams headed clearance dropped to Steven Nasmith, who hurtled towards goal before teeing up McGeady, but after cutting inside onto his right foot he curled his effort wide.
Everton made a double change with just over 20 minutes to go as Steven Pienaar and Romelu Lukaku came on in place of Naismith and McGeady in what were Roberto Martinez's final substitutions.
And the Swans' hopes of coming away from Goodison Park with at least a point were dealt a blow with 18 minutes to go as Shelvey was shown his second yellow card for a foul on James McCarthy.
Everton piled on the pressure, and Jagielka saw his header bounce onto the roof of the net after Lukasz Fabianski had punched clear from a free-kick.
Garry Monk then made his second change as Tom Carroll replaced Sigurdsson as the Swans looked to firm up the midfield, while Nathan Dyer was introduced soon after in place of Jefferson Montero.
The Swans were having to dig deep in order to keep Everton at bay, but they did just that as they saw off four minutes of added-on time - and a late Eto'o effort - to claim a deserved point at Goodison Park.