Meanwhile, Manchester United's reward for overcoming rivals Liverpool is a home tie with Norwich in the Capital One Cup fourth round.
Javier Hernandez's strike early in the second half secured a 1-0 win at Old Trafford, which will play host to the Canaries the week starting October 28.
Birmingham ousted holders Swansea 3-1 and have been handed another home match in the last 16, this time against Mark Hughes' Stoke.
Despite Wednesday night's heroics, the Blues are still considered rank outsiders to regain the title they won in 2011, with United amongst the favourites after drawing Norwich.
"Well, you always want a home draw if you can get it," manager David Moyes told Sky Sports 1.
"Norwich are a good side, they have got a good manager and we will give them every respect."
Elsewhere, Newcastle will welcome Manchester City to St James' Park after overcoming Leeds, while Hull travel to Tottenham just days after heading to White Hart Lane in the Premier League.
Managerless Sunderland play host to Mauricio Pochettino's Southampton, while West Ham head north to take on Sky Bet Championship outfit Burnley.
Martin Jol's Fulham travel to Leicester in search of a quarter-final berth in their tie, due to be played on October 29 or 30.