The Londoners were in control for much of the 90 minutes, especially after Florent Malouda put them ahead in the third minute and when Salomon Kalou made it 2-0 after 26, it was almost already lights out for the visitors.
Malouda's second just after the hour-mark gave the home side the points although they did have a late scare when Matt Derbyshire won a penalty and Seb Larsson put it away to make it 3-1 in the 77th minute.
But Carlo Ancelotti's men did enough in the end to replace Arsenal in second on the table because of goal difference and they are now six points behind title favourites Manchester United thanks to their fifth win in their last six league outings.
Birmingham's season is still in the balance after the defeat as they sit just five points clear of the drop zone in 14th position.
Venue: Stamford Bridge, London Crowd: 40,848 Referee: Michael Jones Yellow cards:CHE - nil BC - Stuart Parnaby 49'
GOAL Things started perfectly for the home side when Paolo Ferreira sent an enticing ball in from the right for Didier Drogba who provided a deadly flick-on for Florent Malouda who was the recipient and fired home from close range in just the third minute.
Frank Lampard came close for Chelsea in the 12th minute with an attempt from just outside the box that just missed the top right corner about eight minutes prior to his teammate Petr Cech making a vital save when Birmingham's Cameron Jerome unleashed a powerful drive which the Czech international managed to turn around the post.
Drogba tried his luck with a dipping, swerving shot in the 24th minute before the Blues went two ahead thanks to a piece of Kalou brilliance. GOAL The Ivory Coast international received a short pass from national teammate Drogba outside the area before making a arced run across the top of the box, beating off some would-be tacklers in the process, and curling a shot between the right-hand post and Ben Foster to make it 2-0.
The 36th minute saw Foster get his left hand to a Drogba attempt after the big striker received a long ball from the Chelsea defence which split two Birmingham defenders but his first-time shot from 20 yards was dealt with by the visiting keeper.
Birmingham kept taking it up to the home side but Chelsea were clearly on top with their forward advances looking much more dangerous as half-time approached.
Chelsea continued on their merry way in the second half and just over 15 minutes in they were 3-0 up when Malouda struck again. GOAL Debutant Ryan Bertran, who had earlier replaced Ashley Cole, was the supplier with a lovely cross from the left flank for Malouda who headed home in the 62nd minute to essentially wrap up proceedings.
After the home side's third goal, a bit of sting went out of the contest apart from whenever Bertrand got the ball as the Stamford Bridge faithful showed their appreciation for the 21-year old left-back.
However, Birmingham managed to claw one back with just over 10 minutes remaining when David Luiz brought down substitute Matt Derbyshire in the area. GOA After some confusion, Swedish winger Sebastian Larsson stepped up to the spot and hammered the ball down the centre of the goal giving Cech no chance to make it 3-1.
Derbyshire had a good chance just under five minutes after the penalty but skewed his shot wide before Chelsea should have scored when opposing keeper Foster inexplicably picked up a backpass from Roger Johnson giving the home side a free-kick from about six yards.
But the ball was teed up for Drogba who put it over the crossbar from close range as the match petered right out at the end.
Chelsea Petr Cech (gk) - Paolo Ferreira, David Luiz, John Terry, Ashley Cole (Bertrand 57') - Michael Essien, John Obi Mikel, Frank Lampard - Salomon Kalou, Didier Drogba, Florent Malouda (Anelka 68')
Subs - Ross Turnbull (gk), Ryan Bertrand (57'), Fernando Torres (67'), Nicolas Anelka (68'), Yossi Benayoun, Yuri Zhirkov, Branislav Ivanovic
Birmingham Ben Foster (gk) - Stephen Carr, Roger Johnson, Liam Ridgewell, Stuart Parnaby (Davies 80') - Sebastian Larsson, Craig Gardner, Barry Ferguson, Keith Fahey - Alexander Hleb (Bentley 70'), Cameron Jerome (Derbyshire 70')