The Welsh side came from behind to earn a point against the Black Cats after the South Korean international cancelled out the former England internationals earlier effort
The South Korea international, back in the starting XI after reaching the Asian Cup final with his country, spent the majority of last season on loan at Sunderland.
And the midfielder, who also had a goal ruled out in the first half, made a decisive contribution when he stooped low to meet Kyle Naughton's cross in the second half at the Liberty Stadium - denying Sunderland what would have been back-to-back league wins for the first time this season.
Swansea were somewhat unfortunate to go into the break 1-0 down after wasting several chances, with Jermain Defoe - who opened his Sunderland account in last weekend's 2-0 win over Burnley - showing his finishing skills with a low drive shortly before half-time.
The hosts' pressure finally told with Ki's header and a draw was no more than Garry Monk's men deserved for their efforts.
A point leaves Swansea in ninth, while Guy Poyet's Sunderland remain 14th.
Swansea, who handed Jack Cork a debut in one of three changes from the 1-0 win at Southampton, engineered the first shot on goal in the ninth minute when Bafetimbi Gomis fizzed a low strike wide of the right-hand post.
Sunderland, who named two changes to the side that beat Burnley including a first league start for Danny Graham since the last game of the 2012-13 season, gradually grew into the game and former Swansea midfielder Jordi Gomez flashed an effort wide.
Their threat proved brief as Swansea reasserted themselves and Gomis was denied by a smart save from Costel Pantilimon, who was out quick to save the striker's low shot after he latched on to Jonjo Shelvey's throughball.
The French striker went close again on the half-hour mark when he stretched to meet a teasing cross from Modou Barrow - making his first Premier League start - with his right foot, but he failed to make clean contact.
It appeared as though the pressure had paid off when Ki side-footed home Shelvey's free-kick, only to see his goal ruled out for offside.
Sunderland made the most of the reprieve in the 41st minute as Swansea's defenders backed off Defoe allowing the England international to fire a clinical strike low into the bottom left-hand corner from 18 yards.
Shortly after the restart Sunderland's Ricky Alvarez - rewarded with a start after scoring in Tuesday's 3-1 FA Cup win over Fulham - thought he should have had a penalty when he was tripped by Ashley Williams in the penalty area.
The hosts continued to enjoy the majority of possession and their reward finally came in the 66th minute when January signing Naughton's cross was met with a diving header from Ki that beat Pantilimon.
Buoyed by the goal Swansea continued to probe and Shelvey bent a free-kick wide from 30 yards.
Sunderland were forced to survive a few anxious moments in the closing stages, but - despite substitute Nelson Oliveira testing Pantilimon's reflexes late on - Swansea were left frustrated in their pursuit of a winner.