Cameron Jerome sat Ninian Park alight in the 17th minute as he burst through to net his fourth goal of the season, but Glenn Hoddle's side hit back through Kenny Miller in the 75th minute.
The visitors were almost gifted a sixth-minute opener when Tony Warner flapped at a cross from Kevin Cooper and the ball struck the angle before being hacked clear.
The nervous Warner failed to gather a tame shot from Cooper minutes later and the loose ball was scrambled away for a corner as Wolves piled on the early pressure.
Out of the blue City opened the scoring thanks to 18-year-old striker Jerome's persistence. A free-kick by James Collins was flicked on by Peter Thorne and Jerome burst past a defender before lashing the ball into an empty net.
The visitors should have levelled in the 34th minute when Miller was left with only Warner to beat but he dithered over his shot and the impressive Collins recovered to clear.
Hoddle switched it around after the interval bringing on Colin Cameron and Mark Clyde and it was Cameron who worked another chance for Miller in the 55th minute but his snapshot flew just wide of Warner's near post.
The introduction of Cameron meant Wolves were more balanced and Miller had a glorious chance in the 67th minute but he headed Lee Naylor's high cross over the home crossbar.
The equaliser finally came in the 75th minute when a Keith Andrews corner was bundled home by Miller from point-blank range as the home defence failed to clear.
The Bluebirds' new loan singing Junichi Inamoto came on five minutes later as City went looking for the goal they needed to take them clear of the relegation zone, but as the game drew to a close it was the visitors who looked more dangerous.