Birmingham, relegated to the Championship last season, advanced to a fourth-round trip to Sheffield United after Wade Elliott scrambled in a 74th-minute winner at the second attempt.
The game had appeared destined for extra-time until Elliott's decisive strike, with neither side able to establish dominance.
But Wolves was made to pay the price when its defence failed to clear a cross and man-of-the-match Elliott pounced.
The Birmingham midfielder's first effort hit the post but when David Murphy steered a shot back towards goal, Elliott was on hand to help the ball into the net past helpless Wolves goalkeeper Dorus De Vries.
De Vries was one of 10 changes Wolves manager Mick McCarthy had made from the side which held Tottenham Hotspur to a 1-1 draw at White Hart Lane last weekend.
In the night's other replay, non-league Wrexham's hopes of a fairytale upset against Championship side Brighton & Hove Albion were dashed in a penalty shoot-out.
The Welsh club had taken the lead with a sublime curling effort from player-manager Andy Morrell on 23 minutes.
But Brighton hit back 13 minutes from time through Ashley Barnes to force extra-time at the Racecourse Ground.
Neither side could conjure a breakthrough in the extra 30 minutes, setting up a penalty shoot-out. The decisive moment came with Wrexham's first penalty, where Dean Keates saw his effort saved by Peter Brezovan.
With Brighton slotting its next four penalties it was left to Craig Mackail-Smith to apply the coup de grace, hammering home his spot-kick to give the Seagulls a fourth-round tie with Newcastle United.