A Steven Gerrard penalty saved Liverpool from defeat at Anfield.
Gerrard came on as a substitute seconds before the break and drove home a spot-kick in the second half to salvage a point.
Liverpool led early on through a David Ngog goal but Christian Benitez nodded the equaliser and Cameron Jerome smashed home a stunning 30-yarder to put Birmingham City ahead until Gerrard's intervention.
Fernando Torres was not included in the squad as Liverpool sought a second win in nine matches but Gerrard was named on the bench.
Lee Bowyer saw an effort from 25 yards fly over the bar for the visitors, but they were soon being pinned back.
Hart saved one Ngog effort before the France Under-21 striker gave Liverpool a 13th-minute lead. Glen Johnson surged down the right, cutting between two defenders before crossing for Ngog to see his first effort blocked by Hart.
The ball flew to Kuyt, and again Hart got his legs in the way to deflect a firm effort.
But when the rebound dropped for Ngog, there was no mistake this time with a close-range volley into the roof of the net.
near post
Johnson almost repeated his role in Liverpool's goal after 23 minutes, this time cutting between James McFadden and Liam Ridgewell before crossing to the near post, where Hart snatched the ball from Ngog's toes.
Liverpool had been cruising to this point, but Birmingham struck back with an impressive set-piece. James McFadden fired a free-kick into the box, Roger Johnson headed back across goal where Scott Dann nodded on for Ecuador striker Benitez to head past Jose Reina from close range.
Hart touched over a Javier Mascherano drive, and Daniel Agger saw a low shot following a corner kicked off the line by Lee Carsley as Liverpool tried to hit back.
Birmingham's Benitez was presented with another opportunity after 42 minutes when he was put clear. But Reina forced him wide and the eventual shot sailed harmlessly wide.
A minute from the break Albert Riera, who had been on a solo bid to score from outside the box at every opportunity, suffered a recurrence of his hamstring injury, and Gerrard was instantly sent on as substitute.
And within seconds Birmingham were ahead when Jerome shook off the attentions of Mascherano to lash a swerving 30-yard effort into the net.
hung on
Lucas and Yossi Benayoun both had shots from the edge of the box, one wide and Hart saving the other. Then Skrtel headed wide from a free-kick.
But the confidence Liverpool had shown in the first half hour had evaporated, with the crowd's anxiety growing. And the errors in possession increased.
Then after 62 minutes Gerrard saw a low header hit Hart's left-hand post from Johnson's cross from the right.
Liverpool were awarded a penalty when Ngog got himself to the byline and looked to hurdle a Carsley lunge, the Birmingham man's foot not touching the Liverpool youngster. Gerrard stepped up to drill home the penalty.
Liverpool lost Benayoun with a hamstring pull after 76 minutes, Ryan Babel coming on.
Gerrard fired over a cross for Ngog to fire wide at the near post before sending an 18-yarder just wide.
With nine minutes left Alberto Aquilani finally got his Anfield debut as a substitute for Lucas.
Birmingham were forced to defend desperately in the final minutes but they hung on for a point.
