Adam Lallana had opened the scoring for Alan Pardew's side in the 50th minute as he curled home from the edge of the box.
But the Premier League side fought back late on and after Lee Bowyer had equalised, Carsley slotted home the winner with just 10 minutes remaining.
Ex-Stoke and Burnley defender Wayne Thomas could have opened the scoring in just the third minute but he nodded Lallana's cross wide of the mark.
Marek Saganowski then went close for the Saints after find himself one-on-one with Blues keeper Maik Taylor but he drove his shot straight into the keeper's arms.
But Alex McLeish's men almost found themselves ahead on the half-hour mark when Christian Benitez rattled the post from the edge of the box.
And Saints keeper Kelvin Davis had to be at full stretch to thwart Seb Larsson on the stroke of half time, tipping his free-kick wide of the mark.
But it was a different story after the break as Pardew's men took the lead. Saganowski played the ball through the Birmingham defence to Lallana and curled an unstoppable effort into the top corner.
Birmingham responded with substitute Garry O'Connor testing Davis from range, but the former Luton shot-stopper was equal to his effort.
But Bowyer drew the Blues level in the 76th minute when he latched onto Benitez's pass and drilled the ball past the despairing dive of Davis.
And Carsley ensured that there was to be no extra-time on the south coast when Stuart Parnaby crossed for the ex-Everton man to ram the ball home from inside the six-yard box.