The visitors were the dominant side in an entertaining first half as they restricted the hosts to two free-kick attempts, but it was all Martin O'Neill's team in the second
Michael Laudrup's side dominated the first half before the tide turned in the second, but Nathan Dyer and Danny Graham went closest to breaking the deadlock in the dying moments.
The hosts remained unchanged from their victory at Wigan Athletic, whilst the visitors opted to put potential Black Cats signing Danny Graham on the bench and brought in Dyer, Dwight Tiendalli, and Itay Shechter at the expense of Wayne Routledge, Angel Rangel and Ki Sung-Yeung.
The early exchanges of the game saw a lot of controlled passing and possession from Swansea and not much from Sunderland.
Dyer was involved with most of the chances in the first half. After a long spell of keep-ball, the wideman played a one-two on the edge of the box but he couldn't quite get the curl he wanted on his shot.
The Swans were a constant threat on the break and it was through Dyer's speed on the counter that nearly brought them the opener. His cross saw touches from Shechter and Pablo Hernandez, but Michu's shot was well-blocked by John O'Shea.
Simon Mignolet was called into action midway through the half, tipping Chico Flores' toe-poke round for a corner as the pressure piled on.
Sunderland's chances in the first half were restricted to two free-kicks, one from Sebastian Larsson - which was punched clear by Gerhard Tremmel - and the other a Craig Gardner effort which was rising over the bar the moment it left his boot.
The hosts started the brighter of the two in the second half and although they weren't carving out chances, they were still putting the visitors under sustained pressure.
The Swans were restricted to clearing their lines as the Black Cats began to push higher and higher up the pitch.
A Jonathan de Guzman free-kick which landed on top of the net almost broke the deadline just before the hour mark, though, as the visitors tried to regain their tempo from the first half.
Subsitute Ki almost immediately repaid Michael Laudrup's decision to bring him on, but his shot from distance was straight at Mignolet.
A quick throw-in from Stephane Sessegnon saw substitute James McClean run at Chico Flores and fall over, but referee Andre Marriner judged the Republic of Ireland international had dived and consequently booked him.
The biggest chance of the game came on the 80th minute. Michu did brilliantly well, winning the ball and playing it straight to Dyer, who in turn played it back. The Spaniard slid the ball back into the path of the little winger but he planted his side-footed effort wide.
Tiendalli thought he had nicked it for Swansea bang on the 90th minute but he couldn't curl his left-footed effort enough, and Michu set up Graham but Titus Bramble put in a brilliant block, as both sides took a deserved share of the spoils.