THE Clarets were held to a fourth draw in five games after Nikola Zigic grabbed a late leveller for Birmingham.
The Blues resisted early pressure from Burnley and took a 1-0 lead into the break after Curtis Davies rose unchallenged to head in Rob Hall's right wing cross.
But Sean Dyche's side roared back with two goals in two second-half minutes.
Danny Ings scored his first goal of the season in only his second start after getting in front of Davies and slotting home from the tightest of angles.
Ross Wallace added a second in as many minutes for the Clarets direct from a free kick for a foul on Ings after Birmingham had conceded possession straight from the kick-off.
The winger crashed the ball in off the underside of the bar from outside the area, with Jack Butland well beaten.
Burnley looked set to see the game out and record their second win in eight games.
But in increasingly difficult conditions as the rain poured down, Michael Duff missed a routine clearance on the edge of the box and Zigic buried a volley.