© PA Photos
The visitors were the first to force the opposition keeper into a save. Bakary Sako lost the ball in his own half in the eighth minute, allowing Paul Caddis to advance and fire in a long range effort that was saved by the fingertips of Carl Ikeme.
Wolves came close to getting the opener after 16 minutes when Sako made his way down the left flank before pulling the ball back to Bjorn Sigurdarson, but the Icelandic striker's effort hit the outside of the post on its way wide.
The hosts did break the deadlock shortly after the half-hour mark, but it came in fortuitous circumstances. Sako's drilled free kick deflected off Marlon King and into the Birmingham net to make it 1-0.
© PA Photos
The hosts continued to push for a second goal, coming close through Sylvan Ebanks-Blake, Sako and Stephen Ward before hitting the woodwork for a second time when Sako's corner was met by Roger Johnson, whose effort deflected off Curtis Davies and onto the bar.
They couldn't find another breakthrough, but comfortably saw out the victory to move up to 16th in the Championship table, while Birmingham remain 19th.