The Black Cats twice went ahead but Swansea, who were also reduced to ten men when Chico Flores was sent off with 20 minutes left, managed to pull back the deficit on both occasions before holding out for a share of the points.
Steven Fletcher scored on his first full start for Sunderland in the 40th minute when he nipped in to take possession of Ashley William's weak backpass before advancing into the area and slotting home past Michel Vorm with a pinpoint left-footed effort.
In stoppage time of the first half, Swansea managed to level in fine style with some lovely build-up passing before Nathan Dyer chipped a deft ball into the path of Wayne Routledge who hammered home the bouncing ball to make it 1-1.
There was plenty of injury-time in the first half following the injury to Neil Taylor which was later reported as a badly broken ankle and that allowed Fletcher to score with a very late second. The seventh minute of injury-time saw the former Wolves star get in behind Chico Flores at the back post to toe home Seb Larsson's free-kick from the left flank.
However, just when Sunderland thought there was a chance they could sneak away with all three points, Swansea's new star Michu bobbed up in the 66th minute to finish Jonathan de Guzman's cross for his fourth of the campaign which eventually netted a point for the home side.
Chico was then sent off for a dangerous challenge on Louis Saha when he lifted his foot near the head of the Frenchman with referee Roger East, officiating his first Premier League game, brandishing a red card. Replays showed though that there was hardly any contact and Saha had made the most of it but the decision had been made and Michael Laudrup's men had to settle for ten men for the final 20 or so minutes.
Laudrup's 100% winning start to life in South Wales was ended but at least the second-placed Swans showed plenty of character to hold off Martin O'Neill's Sunderland side who have now recorded two draws from their two outings.
Liberty Stadium, Swansea - 20,350