An exciting first half saw four goals go in, two from either side, with Peter Lovenkrands opening the scoring for the visitors after just four minutes.
Coventry were level on 20 minutes and ahead after 22 with a fantastic spell in which Cody McDonald and Kevin Kilbane both scored, with Kilbane assisting for McDonald's goal.
Birmingham were level just a minute before half-time, Jonathan Spector scoring from Morgaro Gomis's assist.
The second half saw chances but no more goals as the game went into extra time.
It was the home side who took the advantage just seven minutes into the first period, with Carl Baker netting the winner.