The visiting Bluebirds controlled large parts of the opening 45 minutes, but they struggled to create goalscoring chances.
Birmingham posed more of an attacking threat after the restart and had the chance to take the lead from the penalty spot in the 56th minute. Don Cowie brought down Jordan Mutch inside the area, but Marlon King saw his penalty saved by Cardiff goalkeeper David Marshall.
However, the Blues did take the lead in the 68th minute courtesy of Erik Huseklepp, who converted a cross from Chris Burke inside the area.
Huseklepp's strike looked to have handed his side all three points until Hudson intervened. Birmingham failed to clear a cross from Peter Whittingham and Hudson was on hand to equalise from 12 yards out.
Both sides had chances to score a winner in the closing stages as they searched for the three points that would take them into a play-off spot.
Neither were able to find the net though as the spoils were shared.