It was rough justice for a battling performance from the relegation-threatened Midlands club.
In their last three games against Manchester United, Arsenal and Chelsea, they have been far from outplayed but all they can show from the matches is a single point.
Chelsea, who gave their expensive striker Nicolas Anelka his first start, were often put out of their stride by Blues' determination to take the game to the Londoners.
But the game was decided in the 78th minute. Pizarro, who had been booked only two minutes previously for diving, bravely dived in to head home Juliano Belletti's corner.
Chelsea's hard-earned win means that their manager Avram Grant has now lost only two of the 27 games in which he has been in charge.
Chelsea, who had not lost any of their previous nine Premier League games against Birmingham, could count themselves lucky to escape with the three points.
Without the services of John Terry and Didier Drogba, Chelsea found themselves in real dog-fight in a goalless first half.
Michael Ballack and Claude Makelele set up several promising moves but were thwarted by Birmingham's tenacious spirit and in the face approach.
The Londoners were put visibly put out of their stride as was indicated in the closing stages of the first half when Birmingham were given fresh hope when Petr Cech almost made a calamitous mistake.
Making a weak clearance to the left of his goal he only put the ball to Cameron Jerome who saw his header from 25 yards hit the post.
But the incident undoubtedly lifted Birmingham as they staged a late rally to pressurise Chelsea's often casual defence.
Olivier Kapo saw an effort blocked, while Jerome's goalbound shot was deflected to safety by a Alex to the relief of the Chelsea defence.
Jerome easily outshone Anelka and led his line with a lot of confidence.
Birmingham, however, should have taken a 56th minute lead when Seb Larsson ballooned his close-range shot over the bar following a right wing cross from Kapo.
At this stage Chelsea's defence was often ill at ease and only survived by some good luck.
Birmingham introduced their latest signing, James McFadden, who forced Cech to make the save of the game within two minutes of entering the fray.
But the Londoners robbed plucky Birmingham of a share of the spoils when a determined Pizarro popped up with his winner.