However, they were made to work for the victory in the second period as Wade Elliot reduced the deficit from the penalty spot and struck again in stoppage time to make it 3-2.
Here, Sports Mole takes a closer look at the action to establish whether it was a fair result.
On target 3
On target 3
Was the result fair?
Just about. You could argue that Wolves deserved the three points purely on the basis of their first-half display. They withstood early pressure and took their chances when it counted. While Birmingham were the stronger side in the second period, they were very wasteful indeed.
Dean Saunders's side were excellent in the opening 45 minutes and did not look like a team at risk of relegation. They were clinical upfront and solid at the back, making them good value for that 3-0 lead. They were less impressive in the second period, but still did enough to deserve maximum points.
Birmingham were poor in the first period, defending badly and wasting opportunities upfront. While they significantly improved in the second half, they didn't get any less wasteful in the attack. Lee Clark's side were particularly poor from set pieces, failing to punish Wolves for the amount of free kicks their defenders gave away.
Sports Mole's man of the match
Sylvan Ebanks-Blake: Although the Wolves striker's afternoon was cut short through injury, his contribution won them the match. He showed the exactly the kind of determination you want to see from your strikers, chasing lost causing and putting chances away when they fall to you.
Jack Robinson's blatant handball in the area in stoppage time takes this award. The youngster demonstrated what can only be described as a moment of madness when under pressure, gifting Birmingham with a last-ditch penalty. Lucky for him that his side had a two-goal cushion at the time.
Carl Boyeson had a heated contest to oversee and he made several questionable calls during it. He seemed reluctant to brandish red cards, as both Jamie O'Hara and Robinson were already on cautions when they committed penalty offences. On both occasions, a second yellow card was called for.
Birmingham: The Blues play host to FA Cup semi-finalists Millwall in their next Championship outing.
Wolves: Wolves' quest to remain in the Championship continues with a trip to Bolton Wanderers.