The Midlanders took a 65th minute lead but the Ivory Coast striker, a second-half substitute, scored his 10th league goal of the season.
With seconds ticking away and Chelsea's unbeaten home record this season looking doomed, Chelsea launched another in a series of attacks on the Birmingham rearguard.
Frank Lampard, for the most part a forlorn figure in midfield, collected the ball close to the six-yard box.
In one quick movement he managed to squeezed the ball into the path of Drogba.
The frontman was equal to the pass and curled an excellent, low right-footer, past the hapless dive of goalkeeper Maik Taylor and the ball nestled into the keeper's left-hand side of the net.
It was no more than the Londoners deserved for their second-half performance. Mind it had to be as their first half performance was woeful.
Chelsea boss Jose Mourinho decided that with his side 11 points clear at the top of the league to rest a couple of vital players from this match. Out went Claude Makelele and Ricardo Carvalho and Drogba.
In came Alexei Smertin and Robert Huth - both have played this season, but they had the look of new boys and had a destabilising effect on the team.
But The Blues started reasonably well and after three minutes a swift move saw Damien Duff blast a left-footer on target, only to see it charged down by Matthew Upson.
But from there on in, it was a poor display from Chelsea.
Birmingham, with the unenviable statistic of not winning away from home this year and scoring just two away goals in the same period, came to the Bridge to defend and hope.
They defended well and had acres of hope to cling on to.
The most notable move of the match came on 22 minutes when a trademark Frank Lampard free-kick, 20 yards out, arrowed through the Birmingham wall, but it was met comfortably by Taylor in goal.
A wayward left-footer by Duff enlivened the crowd, but not by much. Joe Cole decided that it was his time to get into the game and he went off onto a jinking run on 33 minutes.
He sliced through three defenders' paths, nut-megging Kenny Cunningham in the process before letting fly a daisy-cutter from just outside the six-yard box, on the left.
The ball went across Taylor's path beating the 'keeper all ends up, but agonizingly for Cole, the ball skimmed the upright and went out of play.
Three minutes later Tiago dispossessed a sleepy Mario Melchiot on the byline and arrowed a left-footer across goal. But Lampard, running into the box late, was unable to get his foot to the ball.
Mourinho decided he had seen enough and made two crucial second-half substitutions.
On came Drogba and Eidur Gudjohnsen and they made the difference.
But it was Birmingham who could have gone in front early in the second period. Petr Cech produced a brilliant reflex save from a Darren Carter left-foot volley on 49 minutes.
The ball fell to Walter Pandiani, but John Terry snuffed out the shot.
A Drogba header and a Lampard shot both went wide as the Londoners pressed forward, but they succumbed to a sucker punch.
A Jermaine Pennant lofted free-kick was launched into the Chelsea area on 65 minutes. Cech misjudged the flight of the ball, thinking it was drifting out of play.
Upson saw it differently and managed to head the ball back into play. Pandiani was first to react and he blasted a right-footer on target.
The ball deflected off Terry and the underside of the crossbar and into the net.
But up popped super sub Drogba to edge Chelsea back into the game and one point closer to a richly deserved Premiership title.
Man of the Match: John Terry - Was in commanding form. As many of his charges produced poor performances, the skipper time after time lifted his team to raise their game.