This was another truly awful display by the home side who now head off to Naples for a Champions League encounter that, if it goes badly, might see the end of Villas-Boas's tenure at SW6. Chelsea went behind before Daniel Sturridge salvaged some pride for the home side.
This was a game where Chelsea needed the early first goal.
Daniel Sturridge showed his footballing inexperience by failing to hit the ground in the Birmingham penalty area after he was clipped by Stephen Carr on nine minutes. Carr, in fact trundled off two minutes later after being clattered by left back Ryan Bertrand. He was replaced by Jonathan Spector.
In a mad two minutes all that is bad about Chelsea this season happened at once, First, a Adam Rooney corner went right across the Chelsea'ssix-yard box before David
Murphy smashed home past Petr Cech with a smart left footer. Then, on 22 minutes, Ramires did what Sturridge failed to do and that was to go to ground under a clumsy challenge from Wade Elliott in the Birmingham area. Up stepped Juan Mata to thump the ball but goalkeeper Colin Doyle produced a brilliant low dive to his right to prod the ball onto his right post and away to safety.
David Luiz showed his attacking prowess on 35 minutes, when after a mazy run in which he was fouled, he took a brilliant dipping free-kick from 25 yards out to which Doyle did well to tip over his crossbar.
With Chelsea struggling to create, it was left to the long-range brigade to try to level the score, and Ramires's 25-yard blaster, after good set-up play by Fernando Torres, was just inches over the Birmingham goal.
Such was the paucity of effort from Torres, that the Spain striker failed to return for the second half. Didier Drogba, fresh from Africa, and a surprise addition to the squad, replaced him.
Nathan Redmond had the first chance of the second half, From just outside the Chelsea area but he blasted high and wide of Cech's crossbar.
Andre Villas-Boas then replaced midfielder Mikel with striker Salomon Kalou on 58 minutes.
Live wire Mata showed excellent control with his left for but screwed his right-foot shot from just outside the visitors' area wide on 60 minutes.
A minute later and the Blues were level. Sturridge, taking up a central position, was perfectly in place to receive an inch-perfect right byline cross from Ivanovic, and the England striker headed home comfortably past Doyle.
A sizzling free-kick by Jordon Mutch almost deceived Cech who reacted late to smother the 25 yarder 10 minutes later.
Frank Lampard entered the fray with eight minutes remaining with Mata suffering the indignation of being replaced.
Birmingham had a glorious chance to win the game with three minutes remaining, Nathan Redmond was sent clear. But the striker produced a feeble effort in the front of goal, much to Cech's relief.
When the replay is played, one wonders if the Chelsea manager will be in charge. on this display it's doubtful. Chelsea: Cech, Ivanovic, Luiz, Ramires, Torres, Mikel, Meireles, Sturridge, Cahill, Bertrand, Mata. Subs: Hilario, Kalou, Bosingwa, Malouda, Drogba, Lampard, Essien. Birmingham Carr Murphy, Ibanez, Mutch, Doyle, Gorris, Elliott, Rooney, Fahey, Redmond, Davis. Subs: Spector, Asante, Bulland, Gnahore, Reilly, Jervis Ref: Martin Atkinson