The Ivory Coast international's quickfire double turned the match on its head to secure the progress of Michael Laudrup's side into fifth round of the FA Cup
Lee Novak gave the hosts the lead with a headed effort 15 minutes in as Swansea struggled to find its feet at St Andrew's, but the introduction of Bony at halftime proved pivotal.
The striker scored twice in in the space of two second-half minutes to stage a comeback that looked unlikely in the opening period, and send Swansea into the fifth-round draw for the first time since the 2008-09 season.
|By Tom Davis
Birmingham tasted victory against the Swans at St Andrew’s in the League Cup back in September and, up until just after the hour mark, looked on course to frustrate its Premier League opponent once again. Lee Novak’s fine glancing header in the first half was deserved and Birmingham could have conceivably been more than one ahead.
But the halftime introduction of Wilfried Bony was emphatic. He changed the game, scoring two in two minutes as Michael Laudrup’s side dominated much of the second period. It was nearly another triumph for the Blues, but on this occasion, nearly was not quite enough.
Lee Clark handed a debut to loan signing Albert Rusnak as he made five changes to the side that lost 2-0 at home to Yeovil Town last weekend, while Michael Laudrup recalled Roland Lamah and Pablo Hernandez after the pair recovered from injuries.
Clark's men broke the deadlock in the 15th minute as Novak got his head to a Paul Caddis cross, flicking the ball beyond Gerhard Tremmel for a fourth goal in his last six FA Cup appearances.
Swansea was struggling to settle, and Hernandez squandered an opportunity to level matters midway through the opening period when he blasted over from a Neil Taylor cross.
Defender Jordi Amat – playing in midfield due to a Swansea injury crisis – showed his attacking deficiencies in the closing stages of the first half, scooping over from close range and wasting a glorious opportunity to equalize.
Intent on transforming his side's fortunes in the second half, Laudrup introduced Bony in place of Hernandez at the interval.
Swansea looked marginally better after Bony's arrival, and he was denied by a last-ditch Mitch Hancox tackle on the hour mark, before firing a low shot straight at Colin Doyle in the Birmingham goal.
But the Ivorian proved to be the catalyst for sparing Swansea's blushes by netting a two-minute brace to turn the tie on its head.
The 12 million pound frontman hammered home a volley from a Lamah cross in the 67th minute, before finishing off an incisive attacking move for his second two minutes later, and Birmingham was unable to bounce back from the visitors' quickfire double.