Cole was red-carded for a lunge on Laurent Koscielny before David Ngog's driven shot put Liverpool ahead.
Birmingham hit back as Liam Ridgewell bundled in James McFadden's cross and survived three late David Ngog chances.
Liverpool finally found some rhythm and David Ngog had a chance to equalise but headed straight at Andreas Isaksson.
Torres was replaced on 65 minutes by David Ngog, who missed several chances as Liverpool pushed for a vital win.
David Ngog swivelled and had a shot blocked by Napoli's Salvatore Aronica as both teams had to settle for a draw.
They have already drafted in Philipp Degen, fellow full-back Andrea Dossena, goalkeeper Diego Cavalieri and teenagers David Ngog and Emmanuel Mendy.
Benitez introduced David Ngog and summer-signing Alberto Aquilani in the latter stages but Arsenal close out the latter stages in relative comfort.
They were eventually made to pay for the miss when David Ngog side-footed in his first league goal for the Reds after Steven Gerrard's headed pass.
Gerrard produced a wonderful piece of magic on the right to find Dirk Kuyt who poked in for 3-0 before substitute David Ngog nodded in in injury time.
"You have Maxi Rodriguez, David Ngog, Ryan Babel, Joe Cole - they are quality players and it is a very strong squad and they look organised, " he said.
But, there were no signs that Liverpool were feeling the effects of their exertions in the week as they started brightly with chances falling to David Ngog, Maxi Rodriguez and Aquilani.
The midfielder cajoled his stuttering side into a greater urgency and, after David Ngog and Raul Meireles missed two gilt-edged chances, it was left to the Reds captain to grab an equaliser.
Houllier admitted that conceding two goals in the opening 16 minutes at Anfield, with one each from makeshift strike-force David Ngog and Ryan Babel, made things very tough for his young side.
French striker David Ngog scored Liverpool's early winner, but Rafael Benitez's side struggled to produce a convincing display, the damage having been done in two games against Lyon that cost them four points.
Joe Cole put the Reds ahead and, while Cristian Tanase equalised for Steaua, Lucas Leiva powered in a long-range strike sandwiched in between two David Ngog goals to wrap up a win for the Merseysiders.
Liverpool had Joe Cole sent off on the stroke of half-time but later took the lead through David Ngog and looked set to hold on for the three points until the visitors were handed a late leveller by Reina.
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Despite Benitez swapping the ineffective David Ngog for Netherlands winger Ryan Babel after 63 minutes, the Dutchman fared little better with the chances he was offered, squandering an excellent opportunity in front of goal four minutes after getting on the pitch.
Liverpool, who were without the injured Steven Gerrard and Fernando Torres, showed their defensive discipline to keep out Spurs and should have been out of sight by the time they were awarded an injury-time penalty after David Ngog was brought down by Sebastien Bassong.
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