Darren Anderton's strike made Liverpool pay as Birmingham claimed their first away win of the season.
Substitute Anderton arrived at the far post to convert Matthew Upson's header in the 77th minute.
Liverpool had a plethora of chances, with Harry Kewell, Dietmar Hamman and Luis Garcia all going close.
But Birmingham missed opportunities themselves, and former Liverpool striker Emile Heskey was the main culprit, wasting three clear openings.
Birmingham's late winner was harsh on the hosts, but they really should have had the game won by the time Anderton popped up.
Liverpool were using the wet surface to spray passes around at pace and after a neat exchange Josemi crossed from the right for John Arne Riise to head wide at the far post.
The Reds were attacking with real intent and Kewell ran with pace as the visitors defence backed off, his 25-yard strike forcing a flying one-handed save from Taylor.
Former Liverpool striker Heskey was making his first return to Anfield after a £6.5m summer move and he met a cross from the right only to steer it well wide from close-range.
Heskey wasted another chance soon after, heading Izzet's free-kick over, before Liverpool responded with Luis Garcia's powerful drive that Taylor tipped away.
The game suddenly burst into life and Hamman headed over, before a ricochet put Luis Garcia clean through, the Spaniard fluffing his lines by crashing his shot way over the bar.
Although Liverpool were enjoying the lion's share of the possession the two teams continued to trade chances.
First Florent Sinama-Pongolle firing wide from Xabi Alonso's cross.
As the play switched to the other end an Izzet corner again found its way onto Heskey's head, but again the England man could only guide his effort over.
Birmingham came out after the break looking lively and both Damien Johnson and Julian Gray were causing the hosts problems down the flanks.
But they should have found themselves behind when Jesper Gronkjaer lazily gave the ball away and Kewell dummied for Hamman to run on on goal, his drive again superbly saved by Taylor.
Riise then got away down the left and sent in a lovely cross towards the penalty spot, where Kewell could only plant his header over the bar.
Liverpool thought they should have had a penalty when Luis Garcia's shot was cleared off the line - possibly with his arm - by Izzet, but Hamman was booked by Uriah Rennie for protesting.
Blues boss Steve Bruce had brought on Anderton for Stephen Clemence just before to bolster their midfield, and it proved an inspired change.
A cross from the right was headed back across goal by Upson and Anderton arrived unmarked at the far post to guide the ball home from just a yard out.
Liverpool probed for a leveller, sub Igor Biscan heading a corner over, but the Blues defence held firm for their first away win in the Premiership this season.
Liverpool: Kirkland, Josemi, Hyypia, Carragher, Traore, Luis Garcia, Hamann (Biscan 85), Alonso, Riise (Mellor 73), Sinama Pongolle (Finnan 65), Kewell. Subs Not Used: Diao, Dudek.
Booked: Josemi, Luis Garcia, Hamann.
Birmingham: Maik Taylor, Melchiot, Cunningham, Upson, Gray, Gronkjaer (Lazaridis 63), Izzet (Clapham 88), Savage, Clemence (Anderton 63), Johnson, Heskey.
Subs Not Used: Bennett, Yorke.
Goals: Anderton 77.
Ref: U Rennie (S Yorkshire).