Victory also extended City's unbeaten league run to five matches, from which they have gathered 11 points - their best run without a defeat under McLeish who was celebrating two years in charge at St Andrew's.
But defeat kept second from bottom Wolves four points adrift of the safety zone and they have now gone eight league games without a victory.
Blues were the dominant force in the opening 45 minutes with Bowyer again impressing in the centre of the park as his side posed the bigger threat and showed more creativity.
Wolves enjoyed more possession after the interval but seldom looked like breaching the visitors' rearguard with Roger Johnson and Scott Dann producing their usual solid performances at the heart of defence.
Birmingham began on the offensive, knocking the ball around in confident fashion, and after two minutes they went ahead through Bowyer.
Christian Benitez and James McFadden linked up well down the right flank with some neat one-touch football before the ball was worked back to Bowyer on the edge of the box.
He spotted recalled goalkeeper Marcus Hahnemann off his line and his chip floated over the head of the former Reading player into the roof of the net.
David Edwards had the chance to level matters after 10 minutes when he got on the end of a cross from Matt Jarvis but he glanced his header past the post.
Back came Birmingham and Bowyer tried his luck from 20 yards out but Hahnemann was able to save comfortably.
Sebastian Larsson found space on the right edge of the Wolves box after a mistake by Richard Stearman but Hahnemann went down to his right to hold onto his shot.
Birmingham were now back in the ascendancy and Cameron Jerome failed to make full contact with a 20-yard shot which did not extend Hahnemann after he had linked up well with the lively Benitez when in plenty of space.
Mick McCarthy decided he had to make a change and brought on Michael Kightly for Greg Halford after 32 minutes with Richard Stearman and Michael Mancienne swapping flanks in the full-back roles.
Blues had strong appeals for a penalty rejected when Jarvis appeared to bring down Dann close to the by-line.
Then Hahnemann pulled off a fine save to turn over a piledriver at full stretch from Bowyer which took a wicked deflection.
McCarthy made another change for the start of the second half with Mancienne replaced by Stephen Ward.
Wolves began promisingly and Kevin Doyle curled a 20-yard drive only a couple of feet wide after Sylvan Ebanks-Blake had set up the opportunity.
Christophe Berra became the first player to be yellow carded after 57 minutes for holding back Jerome just inside the Wolves half.
Kightly needed treatment to his left ankle off the pitch after a clash with Barry Ferguson and, although he tried to carry on, he had to limp off and was replaced by Nenad Milijas.
Larsson drilled a low shot across the face of goal in a rare Birmingham attack and Hahnemann was alert in racing out of his box to fly-hack clear as Jerome threatened to seize onto a long Larsson pass.
Birmingham almost caught Wolves napping on the counter-attack with a 4-3 overlap in their favour but McFadden's shot was deflected wide from Jerome's pass.
Joe Hart made his first meaningful save after 74 minutes with a reflex save to keep out Jarvis' rising shot as City held on with relative ease.