Rafael Benitez made nine changes from the side that beat Reading on Saturday, with Gabriel Paletta and Lee Peltier getting their second Liverpool starts, with recalls for Jerzy Dudek, Stephen Warnock, Daniel Agger, man of the match Bolo Zenden, Mark Gonzalez, Craig Bellamy and captain Robbie Fowler.
Birmingham started the game the brighter, creating a couple of half decent chances inside the first five minutes but after that the Reds got a grip on the game that they never relinquished.
There was a serious blow for Liverpool during the first half when Momo Sissoko was stretchered off with a suspected dislocated shoulder. Sissoko is definitely out of Sunday's trip to Arsenal and could face a couple of months on the sidelines.
It was during the seven minutes of injury time added on after Sissoko was stretchered off that the Reds scored the winner. A Jermaine Pennant corner was whipped into the box and met by Daniel Agger. The Dane's header was blocked but the ball fell to his feet and he hammered home into the top left corner of the net for his second goal of the season.
Liverpool continued to boss the game in the second half and had chances to wrap the game up. The best was a penalty, awarded when Mark Gonzalez was sent flying in the box, but Craig Bellamy's spot-kick was a feeble one and was easily saved by Maik Taylor.
Bellamy had another chance a minute later when Bolo Zenden's pass found him in space in the six yard box only for the Wales international to miss kick.
Birmingham tried to push for an equaliser and Jerzy Dudek was called upon to make a couple of good saves but the Reds' lead was never really in any real threat.