Saints looked set for their second win of the season when Morgan Schneiderlin got on the end of a Rickie Lambert knockdown to force the ball past Gerhard Tremmel after 64 minutes.
But Nigel Adkins' men threw the lead away within 10 minutes when Maya Yoshida was unable to control a short pass from goalkeeper Paulo Gazzaniga and Nathan Dyer pounced.
The former Southampton winger had only been introduced just before the hour mark and produced a clinical finish in off the post to get Swansea back on level terms.
Although the home side pushed for an equaliser their efforts looked tired and both sides were forced to settle for a point apiece.
Having seen his team concede the opening goal in all 10 games so far this season, Adkins had been keen to keep things solid before the break.
And while the Swans dominated possession they created little beyond a near-post drive from Ki after good trickery from the South Korean.
Indeed, Southampton had the better of the openings with Rickie Lambert a useful weapon with his knockdowns. Gaston Ramirez and Schneiderlin both fired wide when well placed.
It was no surprise when the goal came by that route. But it was even less surprising to see Saints throw the lead away and while they climb above QPR they remain in trouble in 19th.
|Southampton||Team Statistics||Swansea City|
|0||1st Half Goals||0|
|4||Shots on Target||3|
|7||Shots off Target||2|
|41.4||1st Half Poss.||58.6|
|56.2||2nd Half Poss.||43.8|