The point was enough to take Kenny Jackett’s side top ahead of the later fixtures – but it was an uninspiring Midlands derby.
Dave Edwards hit the bar for Wolves while Birmingham’s Jonathan Grounds escaped a clear handball in the area.
Koby Arthur and Clayton Donaldson wasted the committed visitors’ best chances in Gary Rowett’s first game in charge.
He made four changes from the side thumped 8-0 at home by Bournemouth last week, 48 hours before his appointment.
In came debutant Michael Morrison, on loan from Charlton, David Davis, Andrew Shinnie and Arthur.
Liam McAlinden started for Wolves after he was recalled from his loan spell at Fleetwood after Bakary Sako, who was on the bench, failed to recover fully from a groin injury.
Nouha Dicko was ruled out with a hamstring problem, with Leon Clarke replacing him up front.
And the striker had Darren Randolph scrambling to turn his looping header over on six minutes.
With plenty of the ball Wolves were able to dictate the play but failed to seriously test a Birmingham side who shipped eight in their last game.
Randolph gathered James Henry’s 18-yard effort but Rowett would have been encouraged by his side’s solid, if unspectacular start.
Slowly though, the visitors did begin to create and Arthur blazed into the side-netting after being left to pick up David Cotterill’s deep free-kick.
And in the 26th minute Donaldson smashed wide after robbing Kevin McDonald as Wolves’ nerves grew.
Without the dynamism of Sako and Dicko the one-dimensional hosts failed to penetrate the visitors and were reduced to long, hopeful, balls going forward.
The pattern continued after the break with Wolves stifled by hard-working Birmingham – although they survived a scare 10 minutes into the second half.
Henry found space and crossed, only for the ball to hit Grounds’ outstretched arm in the area – but Wolves’ strong penalty claims were rejected.
Five minutes later Grounds forced Carl Ikeme into action, the goalkeeper parrying his header from Cotterill’s corner.
But Wolves had been the better side since the restart and McDonald flashed a low drive wide before Randolph tipped Edwards’ header over after he spilled substitute Sako’s cross.
Edwards then chipped onto the bar on 71 minutes as Birmingham retreated and they were indebted to Randolph a minute from time.
Brek Shea was left by Henry and his low cross was smartly kept out by the keeper, with Sako blazing the rebound over.