The Premier League club, who last won the FA Cup in 1955, were shambolic throughout and were booed off at halftime and full time after being outplayed by the visitors who were relegated from the top flight last season.
Birmingham were 2-0 up by halftime thanks to Gary McSheffrey's fifth-minute effort and Nolberto Solano's own goal.
James Milner's long-range effort gave Newcastle a lifeline after 55 minutes but they were reduced to 10 men soon afterwards when Steven Taylor clipped Dudley Campbell just outside the area and from the resulting free kick Bruno N'Gotty made it 3-1.
Sebastian Larsen and Campbell added to Newcastle's misery with further goals to seal a fourth round meeting with Reading.
Fulham looked to be joining Newcastle as Premier League casualties when they trailed 3-1 just after halftime to second division Leicester City.
However, two goals from Italy international Vincenzo Montella, currently on loan from Roma, in seven minutes levelled the tie before Wayne Routledge made it 4-3 to the London club in stoppage time. Fulham will face Stoke City in round four.
There were no such alarms for eight-times winners Tottenham Hotspur who cruised past Cardiff City in their replay at White Hart Lane after the first match ended goalless.
First half goals from Aaron Lennon, Robbie Keane and Steed Malbranque killed the game off and Jermain Defoe, who started the match on the bench, completed the rout after the break.
Tottenham will take on Southend United in the next round.
