But their point came from a huge slice of luck when referee Peter Walton awarded a penalty against Lee Carsley for a tackle on David Ngog that made no contact with ball or opponent.
Birmingham boss Alex McLeish accused the French youngster of diving, and Benitez admitted the penalty should not have been given.
Ngog had grabbed an early lead for Liverpool, who were stunned by two goals before the break by Christian Benitez and Cameron Jerome to give Birmingham the lead.
The penalty came midway through a one-sided second period, with Steven Gerrard - on as a substitute - ramming the spot-kick past Joe Hart.
McLeish was left fuming, saying: "There is no real debate, Ngog has dived to win his team a penalty, it happens in the game and has done for years and years.
"The referee didn't get that one right, and when he looks at it again I am sure he will agree.
"He's an honest enough guy, but he will probably agree that their player dived, and it was a terrific dive. Lee Carsley never touched him."
He added: "Lee dived in, and when you do that there is always a risk. But on this occasion there was no contact. That was not even close to being a penalty.
"I felt we were comfortable, but apart from when Gerrard made a late run to hit the post, I felt my defenders and the whole team were awesome.
"We scored two fine goals, a good set-piece for Benitez to get his first goal for us and then Jerome's cracker. It was a goal from the second it left his foot.
"The players deserve a lot of credit for the way the fought for everything."
And when quizzed on the penalty decision, Benitez conceded his side were fortunate.
He said: "We scored with a penalty that probably wasn't a penalty, but we deserved to win the game.
"It was clear, it was not a penalty, even if that works against us.
"There have been many times this season that we have not been awarded penalties we should have had.
"I have asked Ngog and he said that maybe it wasn't a penalty, either."
Benitez, who now has Yossi Benayoun and Albert Riera suffering from hamstring injuries, revealed that Fernando Torres "did not feel confident to play."
Torres is struggling with a groin problem, and Benitez said: "Torres was not confident, we have now started a three-week course of treatment and we will have to see how he reacts. We are not considering an operation yet."