Barnet grew into the opening half, however, and had a goal disallowed after 25 minutes when Ricky Holmes was deemed to be in an offside position.
Barnet took the lead five minutes later when Jonathan Nurse found the bottom corner, but Birmingham were level after 37 minutes when King converted from the penalty spot.
Holmes had a glorious chance to send Barnet into the lead moments before the break, but he struck the post from close range.
Birmingham did take the lead, however, after 50 minutes when Steven Caldwell tapped home from close range. Meanwhile, it was quickly 3-1 when Darren Ambrose curled one into the top corner moments later.
The home side continued to dominate as the second period advanced - passing up a host of chances to extend their lead - while Holmes remained the away side's biggest threat.