Bees summer signing Jon Nurse headed the League Two visitors into a deserved lead and, after Marlon King equalised from the penalty spot, Ricky Holmes then struck a post in first-half injury time.
But Blues emerged a different side after the break and skipper Steven Caldwell finally broke his City duck in what was his 53rd game for the midlands club.
Darren Ambrose curled home a fine effort before fellow Birmingham new boy Peter Lovenkrands and then Wade Elliott also got in on the act late on to wrap up what was, in the end, an impressive victory for the 2011 winners.
Manager Lee Clark, taking charge of his first competitive game as Blues boss, handed debuts to summer additions Ambrose, Lovenkrands, Hayden Mullins, Ravel Morrison and goalkeeper David Lucas, who was taking his place between the sticks with Jack Butland on England duty.
The hosts started the opening minutes brightly but Barnet soon took the game to their Championship opponents.
And they finally got their just desserts in the 31st minute as Nurse headed Jordan Brown's left-wing cross past Lucas, who should have done better.
Yet Birmingham were back on level terms before the break after King was brought down in the penalty area by Clovis Kamdjo, stepping up himself to send Liam O'Brien the wrong way.
Barnet could have regained their lead in first-half stoppage time as Holmes beat Lucas with a deft chip which came back off the woodwork.
Birmingham moved in front four minutes after the break as centre-back Caldwell smashed home Ambrose's corner from eight yards off the underside of the crossbar.
Ambrose scored five minutes later when he curled a delightful effort into the bottom corner from the edge of the area.
In injury time Lovenkrands bagged his first in Blues colours before Elliott also waded in from 18 yards.