An inspired second half display from Birmingham saw the Swans crash out of the Capital One Cup at the third round stage.
The holders had the better of a goalless first half as Wilfried Bony and Alejandro Pozuelo spurned good chances, while Roland Lamah should have done better when one-on-one with Colin Doyle.
The Blues broke the deadlock shortly after the restart as Dan Burn headed home, before Matt Green doubled the lead with a tap-in from six yards.
And the win - and Birmingham's place in round four - was secured when Chris Burke set up Tom Adeyemi to finish well late on.
The Swans did manage to pull one back in added time, as Bony headed home from Wayne Routledge's corner.
It means there will now be a new name on the Capital One Cup as the Swans now turn their attention to Saturday's Premier League clash with Arsenal at the Liberty.
Michael Laudrup made ten changes to the side that beat Crystal Palace last Sunday, with midfielder Jonjo Shelvey the sole survivor from the 2-0 win at Selhurst Park.
Goalkeeper Gerhard Tremmel took his place in goal, while Neil Taylor returned from injury to line up at left-back in place of Ben Davies.
Shelvey was joined in midfield by Jonathan de Guzman and Leon Britton, Wilfried Bony led the attack, and Garry Monk made his first appearance of the season to captain the side.
SWANS: Gerhard Tremmel, Dwight Tiendalli, Jordi Amat, Garry Monk (capt), Neil Taylor, Leon Britton, Jonathan de Guzman (Alvaro Vazquez, 63), Jonjo Shelvey (Jose Canas, 72), Roland Lamah (Wayne Routledge, 80), Alejandro Pozuelo, Wilfried Bony.
SUBS NOT USED: Michel Vorm, Chico Flores, Ben Davies, Michu.
BIRMINGHAM: Colin Doyle, Jonathan Spector, Dan Burn, Paul Robinson (capt), Paul Caddis, Tom Adeyemi, Callum Reilly, Mitchell Hancox, Chris Burke, Matt Green, Shane Ferguson (Andy Shinnie, 82).
SUBS NOT USED: Nick Townsend, Olly Lee, Scott Allan, Darren Ambrose, Koby Arthur, Peter Lovenkrands
The visitors made a positive start in the Midlands, passing the ball about with ease despite not troubling home keeper Colin Doyle.
It was the home side that had the first effort on goal as Chris Burke fired over the bar from the left corner of the box after a corner had been half-cleared.
However, the Swans were a whisker away from taking the lead on 18 minutes as Wilfried Bony headed Jonathan de Guzman’s corner against crossbar, before Alejandro Pozuelo crashed his follow up volley against the post.
Burke was in the action once more just a few minutes later as his curling shot was easily gathered by Gerhard Tremmel in the Swans goal.
But it was the visitors who came closest once more on the half hour mark as Roland Lamah did well on the right edge of the box before pulling the ball back for an unmarked Bony, but the striker’s shot was superbly saved by the legs of Doyle.
The Ivory Coast international then spurned his third chance of the half just moments later as he cut in from the left and curled a shot a fraction wide of the left-hand post.
Bony was denied another effort on goal ten minutes before the break as Pozuelo played him through on goal, but Dan Burn got back to save the Blues with a fine tackle inside the penalty area.
But perhaps the best chance fell to Lamah just before the interval as he was played in by Pozuelo, but as the winger bared down on goal he was denied by another fine stop by Doyle.
HALF-TIME:Birmingham 0 Swans 0
Neither side made any changes at the break, but it was the home side who came close to opening the scoring just five minutes into the second half.
A long ball was chased down by Garry Monk but as the captain attempted to lob the ball back to Tremmel, it was caught short and Matt Green capitalised before seeing his shot saved superbly by the German keeper.
But it was Birmingham who broke the deadlock on 55 minutes as Jonathan Spector’s cross from the right was headed home by Dan Burn.
And just five minutes later the lead was doubled as Burke played in Mitch Hancox down the left edge of the box and his low cross was tapped in by an unmarked Matt Green.
The Swans then made their first change of the game as Jonathan de Guzman was replaced by Alvaro Vazquez.
But the home side kept pressing and Hancox himself saw a shot deflected over the crossbar, before Green teed up Burke inside the box but he dragged his shot wide of the far post.
The visitors came close to pulling one back with twenty minutes to play as Pozuelo forced Doyle into a smart save, before Jose Canas was brought on in place of Shelvey.
However, Birmingham extended their lead even further with ten minutes to play as Canas gave the ball away outside the box and Burke set up Tom Adeyemi who had the simple task of slotting into an empty net.
Wayne Routledge came on for the final stages in place of Lamah, and Wilfried Bony pulled a goal back in stoppage time, but it wasn't to be for the Swans as the League Cup holders bowed out of the competition.