Birmingham City substitute Kevin Phillips condemned Swansea to their first home league defeat of the season.
Jordi Gomez gave Swansea a 90th-second lead by converting Federico Bessone's cross before Marcus Bent's header levelled for Birmingham.
Angel Rangel's low cross forced Liam Ridgewell to score an own goal before a Phillips double secured a comeback.
The Blues striker scored twice in five minutes, heading home James McFadden's cross before hitting the winner.
Swansea's night of misery was compounded when top scorer and talismanic midfielder Ferrie Bodde was stretchered off in the first half with a suspected serious injury to his left knee.
Bodde's midfield partner Leon Britton was also taken off early with a back problem.
Swansea City manager Roberto Martinez:
"I'm extremely proud of our players as we put Birmingham under massive, massive pressure.
"We had enough chances to win but my concern is how expensive the injuries are going to be over the long term.
"Birmingham had three shots on target and they scored, showing their quality."
Birmingham City manager Alex McLeish:
"We were 2-1 down at half-time and to secure another victory shows our team spirit and character.
"The opening goal knocked the stuffing out of us and left Swansea to dictate the game.
"But Kevin Phillips is unbelievable, that's the only word to describe him. His finishing was amazing and typical of Kevin he makes it look simple."
Swansea: Konstantopoulos, Rangel, Williams, Monk, Bessone, Britton (Scotland 72), Bodde (Bauza 36), Gomez, Pratley, Gower, Pintado (Brandy 80).
Subs Not Used: De Vries, Tate.
Booked: Gomez.
Goals: Gomez 2, Ridgewell 45 og.
Birmingham: Maik Taylor, Hunt, Ridgewell, Jaidi, Queudrue, Larsson, Carsley, Owusu-Abeyie (Phillips 65), Nafti (Agustien 67), McFadden (Jerome 80), Bent.
Subs Not Used: Doyle, Murphy.
Booked: Bent.
Goals: Bent 42, Phillips 74, 79.
Att: 16,956
Referee: Anthony Taylor (Greater Manchester)
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