Goals from Claudio Pizarro, Florent Malouda and Michael Essien saw off the visitors who took a 1-0 lead through Mikael Forssell before Olivier Kapo made it 2-2.
Chelsea's win meant they created a top-flight record of remaining undefeated at home in 64 matches.
But it was Birmingham City, in the shape of ex-Chelsea hit-man Forssell, who had the first goal-bound shot of the game on five minutes but his low drive was well held by Petr Cech.
Chelsea replied three minutes later with a quick counter-attack, which saw Shaun Wright-Phillips send an inch-perfect cross-field ball to Salomon Kalou. He set up Malouda on the edge of the penalty area only for the Frenchman to blast his shot over the bar.
Pizarro's first effort in a Chelsea shirt came on 13 minutes when he met Wright-Phillips' early right-wing cross with a glancing header but Colin Doyle easily plucked the ball out of the air.
A minute later the livewire Wright-Phillips arrowed a crisp right-footer across Doyle's goal.
But it was the visitors that took the lead on 15 minutes when Gary McSheffrey sent in a curling free-kick, centre-back Liam Ridgewell flicked the ball on and the ball zipped off Forssell's head from six yards out past a helpless Cech.
Within a minute though Chelsea were level when Doyle made a hash of a low Pizarro drive after good play by Wright-Phillips.
The Peru striker, on his Premier League debut, fired a low right-footer towards goal but Doyle let the ball slip under his outstretched arms and into the net.
Sustained pressure by Chelsea paid off on 31 minutes when Malouda put the Londoners ahead.
Picking the ball up on the left, he cut inside, played an excellent ball to Frank Lampard, who in turn found Kalou who fed Malouda and he tucked home a smart left-footer past Doyle from six yards out.
Lampard should have scored number three 60 seconds later but a last-ditch stop by Johan Djourou on the goal-line prevented the Chelsea skipper netting.
With ten minutes of the first half left, Kapo got the better of Glen Johnson on the left and arrowed home a vicious left-footer across the body of Cech and into the top left-hand corner of the net.
Excellent close control on 43 minutes by Kalou almost saw him restore Chelsea's lead, but this time Doyle showed a safe pair of hands.
Chelsea retook the lead five minutes into the second half, and again Doyle was at fault.
Essien stole towards the edge of the Birmingham area and received a cut-back from Wright-Phillips. The Ghana midfielder let fly with a curling right-footed drive, which youth team product Doyle allowed to go straight through his hands.
With eight minutes remaining Ridgewell had a free header from Sebastian Larsson's corner but, unluckily for the former Aston Villa man, he failed to get enough power into his effort.
Substitute Didier Drogba then hit an audacious 50-yard blaster, which only just faded at the last minute from going into an empty net.
Chelsea ran the clock down and justifiably won all three points.