Chelsea simply did not have enough guile to get past Blues goalkeeper Maik Taylor, who was easily the man-of-the-match.
Taylor blocked shots from a host of players, not least Frank Lampard on 12 minutes.
But a Jimmy Floyd Hasselbaink fluffed header on 20 minutes signalled the mood of the match.
Chelsea will lament Joe Cole's excellent curling effort from wide just inside the penalty area that had Taylor flapping, and only the left upright prevented the England midfielder from scoring on 22 minutes.
But it was a terrific goal-line clearance on 49 minutes by Oliver Tebily from a William Gallas flick which best summed up Blues' honesty.
It was one-way traffic as far as possession went but Blues did have the odd chance - Robbie Savage should have done better a minute before Tebily's miraculous saving effort.
Savage latched onto a Carlo Cudicini knock-out but shot wide from just inside the penalty area.
"It was backs to the wall stuff at the end," said Blues boss Steve Bruce after the game.
"Chelsea did not underestimate us, but we took the game to them and competed. That's what you have to do in this league if you want to win it or stay in it."
Chelsea: Cudicini, Johnson (Melchiot 81), Desailly, Gallas, Bridge, Cole (Mutu 60), Lampard, Makelele, Gronkjaer (Duff 45), Gudjohnsen, Hasselbaink. Subs Not Used: Sullivan, Huth. Booked: Cole, Johnson.
Birmingham: Taylor, Kenna, Purse, Cunningham, Clemence, Savage, Johnson, Hughes (Kirovski 81), Tebily, John (Carter 89), Morrison (Lazaridis 66). Subs Not Used: Bennett, Barrowman. Booked: Savage, Tebily.
Referee: J Winter (Cleveland).