Lukas Jutkiewicz put Blues ahead with a neat dinked finish in the 32nd minute.
Beforehand Gary Gardner, and then Harlee Dean in the second-half, left the crossbar shuddering with powerful shots from distance.
Wolves missed a great chance before equalising right at the death.
But there was almost another twist as Jutkiewicz glanced agonisingly wide moments before the final whistle.
This match was the main warm-up for Blues ahead of the Championship return on Saturday, at West Bromwich Albion.
Blues have been staging a series of 11 v 11 practice matches at the Trillion Trophy Training Centre, Wast Hills, to fine tune.
Blues also used the opportunity against Wolves to put into place various health and safety measures, adhering to the guidelines of the EFL's behind closed doors Return to Play Protocols.
Both dressing rooms in the tunnel in the Gil Merrick Stand and the areas behind the stand will be used by Blues for the remaining home games.
The visiting side will have use of all the Main Stand executive boxes to change in and base themselves from.
Social distancing was in place throughout around the technical and bench areas with coaches, substitutes and support staff staying apart on the Main Stand trackside and in the Paddocks.