Championship outfit Birmingham grabbed early second-half goals from Dan Burn, Matt Green and Tom Adeyemi to delight the home crowd at St Andrew's after their Premier League opponents had the better of the first period.
Wilfried Bony scored in injury time for Michael Laudrup's side, but it was a case of too little, too late for the visitors.
The 20-year-old, who joined on a season-long loan from Manchester United last week, scored all four goals in their win at St Andrew’s on Saturday but cannot play in cup competitions due to a clause in his contract.
But despite the youngster’s absence, Birmingham created the first goalscoring opportunity of the game after 13 minutes when Chris Burke fired over the bar from the edge of the area.
Roland Lamah was next to have an effort on goal for Laudrup’s men, but his shot was kept out by the feet of Birmingham keeper Colin Doyle as half-time drew in.
Laudrup then opted to make changes in an attempt to change the flow of the game, with Alvaro Vazquez and Jose Canas replacing Jonathan de Guzman and Shelvey.
But Birmingham were rampant by this point and increased their advantage when Adeyemi capitalised on a Canas error to claim the third with less than 10 minutes remaining.
Bony then headed home from a Wayne Routledge corner in the dying seconds, but this was no more than a consolation for Laudrup's side.
