The game was played at Birmingham's Wast Hills training ground and it was the home side who went in front with a header from giant Serbian striker Nikola Zigic.
American centre half Will Packwood doubled the lead on the stroke of half time with a spectacular half volley but the Clarets came back into it with a goal early in the second half.
An own goal restored Birmingham's two goal advantage but the Clarets came back to scored a second but despite all efforts couldn't find an equaliser.
Blues' coach Richard Beale said of Burnley: "They've got a good set of young lads who put us under a bit of pressure so it was a good test for us."
The Burnley goals were scored by Cameron Howieson and Micah Evans.