The Tangarines drew 2-2 on the night at St Andrew's to clinch a 3-2 aggregate victory and set up a high-stakes final with West Ham United next week.
Goals either side of halftime by Steven Dobbie and Matt Phillips put the visitors 2-0 up in the semi-final second leg but Birmingham refused to be beaten on the night and fought back through Nikola Zigic and Curtis Davies.
Defender Davies ensured a nerve-jangling finish when his powerful close-range header in the 73rd minute made up for his own goal in the first leg.
"I'm so proud of my players," Holloway told Sky Sports. "That was a fantastic fightback by Birmingham and it was all so exciting that I had to ask someone what the score was.
"It's all over now though. We did it and we are going to Wembley."
West Ham, relegated last season along with Blackpool and Birmingham, take on Holloway's team at Wembley on May 19 for a place in the Premier League in a tussle known as the 'richest club match in football' because the financial rewards for promotion are enormous.
"This has been a real tough day for us," said Birmingham manager Chris Hughton. "I've just walked away from a devastated dressing room - we all feel that way because it's been a long, hard season.
"We've had lots of ups and downs, lots of emotion, and it makes it even tougher when you get so close to reaching the final and miss out."