Keen to maintain their impressive 100 per cent home record from the start, the Bluebirds went in search of an early goal and after only three minutes a speculative effort from 20 yards by Craig Bellamy cleared the crossbar.
Craig Noone then tried his luck from distance, but again with the same result from his 18-yard effort.
The hosts were making all the early running but Lee Clark's side almost broke the deadlock after 14 minutes when a free-kick was floated into the danger zone by Keith Fahey and Leroy Lita's header brought a parried save by Cardiff keeper David Marshall.
The striker wasted another opportunity four minutes later after shooting tamely over the bar when well placed only 12 yards from goal.
Birmingham gradually grew into the contest as the half progressed and the hosts were reduced to shooting from distance, with a Mark Hudson effort sailing wide.
The Bluebirds came closer 10 minutes from the break when Aron Gunnarsson brought a straightforward save out of Blues keeper Jack Butland.
And Cardiff got their noses in front after 39 minutes when Gunnarsson's cross was met by Mark Hudson and Bellamy did the rest from 12 yards out.
Bellamy then saw a 30-yard free-kick clear the bar as the Bluebirds went for a crucial second just before the break.
The hosts continued where they had left off after half-time and Heidar Helguson connected with Noone's cross only to see his effort pass over the bar.
It looked like proving a costly miss after 54 minutes, when Wade Elliott's cross was turned home by Lita from six yards out.
It was no more than the visitors deserved after their considerable efforts to restrict the Bluebirds.
But they found themselves behind again within three minutes when Hudson latched onto a Peter Whittingham cross to net from close range.
Cardiff went on the trail of a decisive third and after 61 minutes Joe Mason's 12-yard effort was again too high to trouble Butland.
It was Mason again who saw an 18-yard attempt blocked by Birmingham's Steven Caldwell, but at the other end Andrew Taylor was forced into decisive action to get in the way of a Keith Fahey effort.
The impressive Mason saw an effort brilliantly tipped around the post by Butland as Cardiff looked the side most likely to add to their tally.
Bellamy went close again with 14 minutes left, Butland again coming to the rescue for the visitors by clawing his effort away from goal.