Blues almost took a second-minute lead over a youthful Black Cats side when Cameron Jerome ran on to Lee Bowyer's long-ball forward but the Simon Mignolet came to the visitors’ rescue with a decent stop with his feet.
Sunderland responded and Ben Foster was called into action by Lee Cattermole before Roger Johnson got in the way of a Stephane Sessegnon shot, but they suffered a huge setback when Birmingham when ahead four minutes before the break.
Both Mignolet and Phil Bardsley left a Jerome flick-on to each other and Sebastian Larsson, who looks set to leave Blues this summer, pounced on the loose ball to fire his side in front.
The Black Cats started the second half brightly as they looked for an equaliser, Jordan Henderson curling into the side-netting following neat one-touch passing from Asamoah Gyan and Danny Welbeck, and Bardsley then brought a brilliant diving save out of Foster.
But once again they failed to make their chances count and were punished with 24 minutes to go when Alexander Hleb beat a couple of men and laid the ball off for Craig Gardner to wrap up the points.