Wolves saw the majority of the possession early on, and had a chance to take the lead inside the opening 10 minutes when Leon Clarke tried to find the target, only to see his effort deflected behind.
Darren Randolph had to remain alert in the Birmingham goal as Liam McAlinden also looked for an early goal, but the Birmingham keeper got down low to make the stop.
The visitors, who are playing their first match under new manager Gary Rowett, started to see more of the ball before half time, with Koby Arthur having their first real chance of the match, slicing just wide after David Cotterill curled the ball in from a free kick.
David Davis tried to set up Clayton Donaldson as the visitors continued to enjoy a strong spell, but the striker's finish was just wide of the post.
Birmingham continued to create the better of the chances as half time approached, but they could not break the deadlock before the break.