With the scores level at 1-1 after 62 minutes Curbishley threw on Francis Jeffers in the hope that the former Everton and Arsenal striker would score the winning goal for the home side.
But instead Jeffers turned provider, setting up the two goals which finally sent the Blues to defeat.
Charlton certainly deserved their victory and should have been more than a goal in front at the break, but their failure to kill off the opposition proved costly when Birmingham equalised early in the second half, before the Addicks' attacking intent after the substitution brought the reward of three points.
This was Charlton's first Premiership victory over Birmingham at The Valley and the visitors don't seem to enjoy the London air, they have won only once in the capital in their last 16 visits and they fell behind after nine minutes to one of the most bizarre goals of the season.
Charlton's Moroccan international defender Talal El Karkouri took a free-kick from 45 yards out and incredibly it evaded everybody and finished up in the bottom of the Birmingham net to make the Charlton central defender the leading goalscorer this season, having found the net on five occasions.
He could have had a second with a brilliant header but for a fabulous save from Birmingham keeper Maik Taylor.
Birmingham's only first-half effort was a Stephen Clemence shot which Shaun Bartlett cleared off the line for the home side.
Charlton were stunned ten minutes into the second half when City equalised with a firm header from Mario Melchiot following Darren Anderton's corner, the first goal for the defender since his move from Chelsea.
But Charlton restored their lead when Jeffers did well to cut the ball back from the goal-line and Bartlett slid in at the far post for his first goal since November.
The third Charlton goal came from an incisive break, Jerome Thomas feeding the ball to Jeffers, whose perfectly weighted pass put Danny Murphy clear for the former Liverpool man to fire home.
Man of the Match: Danny Murphy - Now showing his class having settled down into the Charlton side after his summer move from Liverpool and he scored an excellent goal to put the icing on a home victory.