Jayden Reid scored both, in either half, and when Wolves were reduced to 10 men on the hour they seemed a good bet to see it through for the win.
But Renat Dadashov equalised in the 75th minute and thereafter Blues couldn't break down their local rivals.
Maikel Kieftenbeld got 73 minutes under his belt as he continued his comeback from injury - and he came close to scoring moments before his planned withdrawal.
Blues also fielded a very young team with Daniel Djurovic (16) making his Under-23s debut at left-back, Josh Williams (17) getting his first start, as well as Rhys Hilton.
Williams unfortunately had to come off in the 18th minute after taking a bang to the head so Alfie Chang (17), another who was on duty for the Under-18s in the FA Youth Cup the evening before, also made his debut.
A first moment of alarm came in the fourth minute when Luke Curdle got free in the box from a nod down but Ben Forrest was alive to the danger and scooted round to mop matters up.
Williams, after a robust run down the wing, was halted by a clutch of Wolves player and as he went over took a whack and had to be replaced due to suffering the effects of whiplash and dizziness.
Moha Ramos made a good low stop from a Dadashov effort from inside the area and as Curdle followed up Mitch Roberts got an excellent block on the shot.
Blues first threatened after Kieftenbeld intercepted the ball deep in Blues own half and then Reid moved play to the left for Hilton, who cut back into the box and let fly, only to have his effort deflected wide.
In the 29th minute Ramos was at full spring to tip over a free-kick by Ed Francis that went up and over the wall and was dipping in.
Then Forrest came the the rescue with a brilliant tackle on Dadashov, who got clean through onto a ball that went down right channel. He was bearing down on Ramos when Forrest, closing in at a rate of knots, executed a slide tackle that got the ball away and behind just as Blues deadline day loan target was about to pull the trigger.
Ramos nudged another shot over, from Jack Scott, before Blues took the lead, in the 39th minute.
Miguel Fernandez picked the ball up in the centre of the park and slotted it behind the Wolves defence for Reid to charge on. Reid found the bottom corner as he closed in on goal with a precise left footer.
Blues, though, squandered that advantage in the second minute of added-time when a cross from the right was glanced away but perfectly for Taylor Perry, who crashed the ball into the top corner on the full with his left foot.
Kieftenbeld, who came through the game fine and looked sprightly, was yellow carded 36 seconds into the second-half for a typically ferocious tackle that left Perry in a heap.
Blues restored their lead in the 49th minute, through Reid once more. This time a fantastic raking pass by Ryan Stirk sent him in, down the right-hand side. Reid kept his calm and focus and rifled a low right-footer across the 'keeper and inside the far post.
That's five goals in his last four games, and eight for the season in total.
Blues caused was aided in the 60th minute when Chem Campbell inexplicably punched at a left wing cross as he challenged Ramos and the defence in the air. Having being booked for diving in the first-half, he left the referee with little option but to brandish red.
Three minutes before he was substituted, Kieftenbeld was agonisingly close to seeing off Wolves.
Reid turned the ball to George Baker on the right and he surged forward before setting a pass back for Kieftenbeld, on the edge of the area. The Dutchman connected crisply with his sidefoot but a sweeping shot took the slightest of nick off a defender and zoomed just wide of the post.
Josh Dugmore came on for his Under-23s debut (as Kieftenbeld's replacement), as did Bernard Sun.
Two minutes later Blues were caught out when Dadashov peeled off to the left to collect a long ball forward. Despite being outnumbered and near the byline, he managed to wheedle his way diagonally across the box, delaying his shot on three occasions to commit defenders to ground, before finally bashing it past Ramos from 12 yards.
It was a decisive moment as despite Blues camping out in Wolves half from then on to the finish, they could not break the old gold and black down and fashion a clear cut chance from which to regain the lead.
Blues: Ramos, Baker, Djurovic, Mitch Roberts, Forrest, Stirk, Kieftenbeld (Dugmore 73), Williams (Chang 18), Fernandez (Sun 73), Hilton, Reid. Subs not used: Rouse, Zohore.