Fulham dominated the second period but home keeper Joe Hart had only one worthwhile save to make in an instantly forgettable contest.
The goal was created by Blues midfielder James McFadden who was one of the few players to show much quality and did not treat the ball like a red hot potato.
Bowyer also re-emphasised how important a player he has become for City in the centre of the park since making permanent his loan move from West Ham in the summer.
And, when Fulham upped their performance level after the break, they found centre-backs Roger Johnson and Scott Dann in commanding form and totally committed to the cause.
Clint Dempsey posed the biggest threat for Fulham but there was little to enthuse about from either side and Blues will just be grateful to have pocketed the three points in their bid to secure top flight survival.
Birmingham recalled midfielder Barry Ferguson who had been suspended for the 2-2 draw at Liverpool in place of the injured Teemu Tainio.
Fulham boss Roy Hodgson made three changes from the side that earned a 1-1 draw at Wigan.
Stephen Kelly, a former Birmingham player, Zoltan Gera and fit again Simon Davies were recalled in place of John Pantsil, Damien Duff and the ill Erik Nevland.
The first reasonable opportunity fell to Fulham striker Bobby Zamora who cut in from the right flank virtually unopposed but his left-footed shot flew well wide of the far post.
Birmingham threatened for the first time when James McFadden's left-wing centre picked out Cameron Jerome but his header flew straight at Mark Schwarzer.
Then after 16 minutes City's leading scorer Bowyer put the home side in front with his fourth goal of the campaign.
McFadden was the creator with a deft pass over the top of the Fulham defence.
Bowyer timed his run perfectly to stay just onside before cleverly hooking his shot over the advancing Schwarzer into the corner of the net.
Fulham tried to respond and Gera had a long range effort deflected for a corner and Birmingham centre-back Dann blocked a powerful shot at close range from Paul Konchesky.
Dann's back four colleague Johnson also flung himself at full stretch to get in the way of a drive from Gera just inside the box.
In a rare Birmingham attack, Schwarzer tipped away a testing cross from the impressive McFadden at full stretch with Jerome waiting to pounce.
Fulham looked sharper at the start of the second period and enjoyed the the lion's share of possession.
But it was 13 minutes into the second period before there was a semblance of a chance for either side.
Zamora got up well to chest down a left-wing cross from Konchesky but Gera failed to make proper contact on his shot which bobbled wide.
Bowyer became the first player to be yellow-carded after 67 minutes for a mis-timed challenge on Dempsey.
City keeper Hart was called upon to make his first meaningful save after 70 minutes when he tipped over a powerful Dempsey header from a Kelly centre.
McLeish made his first substitution a minute later, bringing on Keith Fahey in place of the ineffective Christian Benitez.
Duff was brought on by Hodgson with Kelly making way for the Republic Of Ireland international who instantly flashed a drive just wide.