Although the Foxes totally dominated the match it was Birmingham who opened the scoring in the 12th minute through Matt Green. The former Mansfield striker netted from close range to score his first goal for Birmingham.
Leicester wasted plenty of chances before Jamie Vardy finally scored a 78th-minute equaliser. Andy King struck a second four minutes later on his 250th appearance and David Nugent netted from the spot in stoppage time.
Substitute Chris Burke then scored a let consolation goal for Blues.
Pearson said: "It was a good three points although we made heavy weather of it. We wasted a lot of good chances to score and conceded with their first meaningful attack. So it looked as though it was going to be a potentially frustrating afternoon.
"But we were able to come from a losing position to win the game and I was really pleased with the response from the players in the second half.
"Our first league game at home was a dour affair but today we played two different systems and found the answers to the problems the opposition set.
"The players responded well and those who went on in the second half played a big role in changing the fortunes of the side. It was good to see the strikers on the scoresheet as well."
Birmingham manager Lee Clark admitted it was like the Alamo at times as he watched his team lose after taking a one-goal lead.
The Blues had held out in the first half but conceded three late goals and
Clark said: "I warned the players at half-time that we had to do something different. We were leading 1-0 but it was like the Alamo at times the way we were having to defend.
"We had to keep the ball better and do better things. Then we had a good spell in the second half when he needed to be more ruthless. But I have been saying exactly the same things at every press conference.
"Unfortunately there is nothing financially in the way of changing things. We have just got to work hard and try and improve it. We need more at the top end of the field. But as I've said there are no finances. I've got no money.
"I think the foul on David Nugent earlier was more a penalty than the one that was given. The referee was getting stick off the fans and was desperate to give something. I said to the players to be aware of the situation and not commit ourselves to any challenges. I am feeling frustrated but I still feel that, given time, I will get it right. I don't believe there is anyone who can do it better."