Bafe Gomis scored his third goal in as many games as the Swans were held to a 1-1 draw at Sunderland.
The French international coolly slotted home the opener in the final minute of the first half after a fairly indifferent 45 minutes of football at the Stadium of Light.
But despite dominating the second period, the Swans were pegged back by the hosts when Jermain Defoe equalised for Sunderland in the 62nd minute with a calm finish past Lukasz Fabianski.
There were chances to win the game at either end late on, but the spoils were shared as the Swans remain unbeaten after three games.
The Swans remained unchanged from the home win over Newcastle the previous week.
A draw at Chelsea and victory over Newcastle United meant the Swans collected four points from the opening two games, while Sunderland were looking to pick up their first point of the campaign.
Former Sunderland loanee Ki Sung-Yueng missed out again as he continued his recovery from a hamstring problem, while ex-Swans striker Danny Graham started for the hosts.
Costel Pantilimon, Billy Jones, Patrick Van Aanholt, Lee Cattermole, Jack Rodwell, John O'Shea (capt), Jeremain Lens (Seb Larsson, 90+1), Jermain Defoe (Duncan Watmore, 86), Danny Graham (Steven Fletcher, 67), Yann M'Vila, Sebastian Coates.
Vito Mannone, Wes Brown, Adam Matthews, Emanuele Giaccherini.
Lukasz Fabianski, Kyle Naughton, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Jack Cork, Jonjo Shelvey, Gylfi Sigurdsson, Andre Ayew, Jefferson Montero, Bafe Gomis (Eder, 76).
Kristoffer Nordfeldt, Angel Rangel, Kyle Bartley, Leon Britton, Nathan Dyer, Wayne Routledge.
There was little to mention of the opening 20 minutes at the Stadium of Light as both sides struggled to find any kind of fluency in the game.
It was the Swans that saw the first sight of goal as Andre Ayew fired wide of the target from 25 yards, before Sunderland duo Jeremain Lens and Lee Cattermole received yellow cards for robust challenges on Neil Taylor and Ayew.
Ashley Williams was then called into action midway through the first period to deny ex-Swan Danny Graham a header on goal with an excellent last-ditch interception.
At the other end, Bafe Gomis saw a 30-yard effort comfortably held by Costel Pantilimon, before Ayew - who was beginning to prove a menace for the Sunderland back line - dragged wide of goal from 20 yards following a surging run from deep.
In the 35th minute, Graham attempted an audacious over-head kick after Lens’ free-kick dropped invitingly in the box, but his effort was straight into the arms of Lukasz Fabianski.
Just as the half appeared to be petering out, Gomis struck home his third goal in as many games, latching onto Kyle Naughton’s threaded pass before slotting his shot past Pantilimon.
HALF-TIME: Sunderland 0 Swans 1
For what would have been the third match in a row, Ayew almost accompanied Gomis' name on the scoresheet six minutes into the restart when he met Jonjo Shelvey's cross with a thunderous cross, which cannoned off the inside of the post.
Jefferson Montero then tested the reactions of Pantilimon as he cut inside from the left before firing a low shot at the Sunderland stopper.
The Swans were beginning to crank up the pressure on the hosts' defence as Ayew came close again to doubling Swansea's advantage, but this time his glancing header drifted wide of the far post.
But against the run of play, Sunderland were back on terms in the 62nd minute as Jermain Defoe slotted past Fabianski after the Swans were dispossessed in their own half.
Pantilimon was then forced into action to keep out edge-of-the-box efforts from Shelvey and Gylfi Sigurdsson, before the Black Cats goalkeeper showed outstanding reactions to deny a Gomis header from point-blank range.
Ayew and Coates had chances for either side in the closing stages, while substitute Seb Larsson was brought on in added time for his set-piece expertise, but the midfielder hit the wall from a free-kick in dangerous territory with the last kick of the game.