In the day's other sixth round tie Fulham, bidding to reach the FA Cup final for the first time since 1975, played out a 0-0 draw with London rivals Tottenham Hotspur at Craven Cottage.
Portsmouth, bottom of the Premier League and facing almost certain relegation after going into administration, moved ahead in the second half when Piquionne took advantage of a collision between goalkeeper and defender to scramble the ball in.
Piquionne, the on-loan French striker who had scored in their last two league games, got the second when he ran on to a Jamie O'Hara pass, mesmerised defender Roger Johnson with two turns and blasted confidently beyond goalkeeper Joe Hart.
"There's no team that deserves to be at Wembley more," Portsmouth manager Avram Grant told the BBC. "I'm so proud. People have no idea what it's like to work day by day with these difficulties."
The incident came a matter of minutes after the sport's rule-makers announced they had ruled out introducing video technology to decide on such issues.
"I'm an advocate of it (technology) so I'm frustrated by FIFA's decision and not because of what happened today," said Birmingham manager Alex McLeish.
"We have it in other sports and I can't see why we can't have it, especially at the top level."
Zoltan Gera's header just after the break, well saved by Tottenham keeper Heurelho Gomes, was the closest the hosts came to scoring while the visitors had lots of possession but no clear chances and they must now replay at White Hart Lane.
