كتب : Sherif Tarek
The leaders had quite a few scoring chances but Birmingham's in-form keeper Joe Hart produced fabulous saves to keep a clean sheet.
Chelsea defender Alex could have broken the deadlock; his free-kick hit the crossbar though.
On the other hand, hosts Birmingham had a Christian Benitez goal disallowed for offside in the first period.
Chelsea wide man Florent Malouda was dismissed in the dying minutes for two bookable offences either side of the interval.
After salvaging a draw, minnows Birmingham, who are now in seventh spot, extended their unbeaten run to 10 matches.
Chelsea are now five points clear on top of the table, even though they won only one league game out of their last five.
Second-placed Manchester United will close to within two points of the Blues should they register a win at Hull City on Sunday.