Didier Drogba salvaged a point for Chelsea eight minutes from time after Walter Pandiani's goal had threatened to give Birmingham all three points.
Drogba side-footed home from Frank Lampard's pass to keep the Blues' unbeaten home league record intact.
Birmingham had taken a shock lead, Pandiani slamming in after Petr Cech misjudged a free-kick and Matthew Upson had headed the ball back across goal.
Joe Cole hit the post for the hosts in an otherwise lifeless first half.
The draw, coupled with Arsenal's win at Middlesbrough, means the gap at the top is cut to 11 points, but with only six games left Chelsea need only six more points to secure their first title since 1955.
After witnessing a thrilling Champions League tie on Wednesday, the Stamford Bridge faithful were treated to first half that was short on entertainment and quality.
Even the presence of Jose Mourinho on the Blues' bench could not inspire the Champions-elect, with sloppy passing the trademark of the opening 45 minutes.
Only Cole - on Friday named March's premiership Player of the Month - looked likely to trouble the Birmingham defence, slaloming through the defence only to see his shot clip the outside of the post.
If the majority of the crowd thought things would have to improve after the interval they were right, the game bursting into life straight from the restart.
Eidur Gudjohnsen somehow managed to head over from three yards after John Terry had headed a corner goalwards, before Birmingham gave a warning of their own attacking threat.
Midfielder Darren Carter saw his screaming left-foot volley parried by Cech, Terry then bravely blocking from Pandiani before Robert Huth eventually cleared.
Chelsea responded with Drogba heading Damien Duff's cross over while Lampard swivelled and lashed a left-foot shot wide, failing to recreate his wonder goal against Bayern in midweek.
And then Birmingham silenced an already muted stadium. Upson headed a free-kick back across goal and Pandiani rifled in despite Terry's best attempts to block.
Steve Bruce's side looked as though they had studied Chelsea's imperious defence as they successfully repelled an onslaught from Mourinho's men.
But they could not hang on until the end, Lampard feeding Drogba to side-foot the ball into the corner past Taylor from close-range.
Chelsea manager Jose Mourinho:
"It was difficult, we didn't start well and we gave away the first half. We didn't play football, it was at a low pace and low on quality.
"The second half was different, we put pressure on, created chances, but they fought a lot and defended very well.
"The players are not robots. they need mental rest as well as physical. It's not easy after the Champions League."
Birmingham boss Steve Bruce:
"The way we defended, I thought we were comfortable. We were even a bit disappointed not to win but I suppose a draw here's not bad.
"With 10 minutes to go you're thinking can we go on and do it? But I thought we thoroughly deserved the point.
"You know that they've got such quality, they're a class act, but I'm proud of my lads, they deserved it."
Chelsea: Cech, Johnson (Jarosik 69), Huth, Terry, Gallas, Lampard, Smertin (Gudjohnsen 45), Cole, Duff, Tiago, Kezman (Drogba 45).
Subs Not Used: Ricardo Carvalho, Cudicini.
Booked: Cole, Tiago.
Goals: Drogba 82.
Birmingham: Maik Taylor, Clapham, Cunningham, Upson, Melchiot, Pennant (Gray 80), Johnson, Carter (Lazaridis 60), Nafti, Heskey, Pandiani (Morrison 87).
Subs Not Used: Blake, Vaesen.
Booked: Cunningham, Nafti.
Goals: Pandiani 65.
Ref: C Foy (Merseyside).