Portsmouth, cup winners in 2008, will return to Wembley for the semi-final and the cash windfall will come as a huge bonus for a club who face extinction with debts of £76million.
Birmingham matched Portsmouth until Piquionne's first goal in the 67th minute.
However, they had cause to complain when Liam Ridgewell had a goal wrongly disallowed with 10 minutes remaining.
A dull first half was enlivened only by a sharp save by David James in the 16th minute after getting down to his right to hold Cameron Jerome's low shot.
But once Portsmouth had gone ahead, Birmingham's challenge faded and beleaguered Pompey held on for a semi-final which could be worth more than £500,000 to them.
The opening goal was a messy one with Birmingham goalkeeper Joe Hart and defender Scott Dann failing to clear Piquionne's first shot and paying the penalty when he stabbed in from a yard out.
Birmingham were still reeling when Jamie O'Hara, who is on loan from Tottenham, threaded through a pass for Piquionne to twist away from Roger Johnson's challenge to score from 10 yards.
Birmingham manager Alex McLeish sent on veteran Kevin Phillips in a bid to boost his failing attack and the move should have paid off with a goal.
With Birmingham committed to attack, Ridgewell's close-range header was clawed back from the line in the opinion of referee Steve Bennett and his assistant.
However, video replays clearly showed Ridgewell's header had crossed the line and the goal should have stood.
Piquionne might have got a third in stoppage time but was denied a hat-trick by a desperate defensive tackle by Johnson.
At the final whistle, Portsmouth manager Avram Grant raised his arms in triumph and the team received a standing ovation that lasted several minutes.