They now have to visit fellow strugglers, Fulham, and complete the season with a final game against Blackburn.
Birmingham were a "different" team from that which was embarrassingly hammered 5-1 by arch rivals, Aston Villa, in their previous game but they failed miserably to hang on to their hard-earned advantage.
There was a determination to make amends in what was a dire situation with them anchored in the bottom three but it badly back-fired as Liverpool finished on a high note.
To their credit they played with a lot more flair in front of their home fans. The return of Forssell to lead the attack gave them more penetration against a Liverpool side which rarely played at full stretch in the first half.
Liverpool, currently in between their two crucial Champions League games with Chelsea, made only one change from the side which beat struggling Fulham.
They were unable to assert themselves as Birmingham strived to make an impact. Forssell posted an early indication of Birmingham's bid to boost their survival hopes with a shot on the turn which was easily saved by Pepe Reina.
Surprisingly Liverpool's defence did not man-mark their opponents and this allowed Birmingham a great deal more scope than against Aston Villa.
James McFadden was always alive to the knock-on and the Scot appeared to relish the challenge of facing the star-studded Liverpool side.
It was McFadden who carved out Birmingham's opening goal in the 34th minute. He wandered out to the right and produced a great cross which was deflected on by Martin Skrtel to the unmarked Forssell who lashed his shot with great purpose past Reina for his eighth goal of the season.
Nine minutes into the second half Birmingham's hopes were raised even higher when Larsson lashed a rising free-kick past Reina after McFadden had been brought down by Skrtel.
Suddenly Birmingham began to panic in defence and Jermaine Pennant went on a run which ended with Andriy Voronin slipping the ball to Crouch to shoot first-time past Maik Taylor in the 63rd minute.
Liverpool stepped up the pace and a cross from Lucas Leiva in the 76th minute found Benayoun who saw his shot deflected by the unfortunate Radhi Jaidi past Taylor who was moving in the opposite direction.