Iain Dowie’s side had been thumped 4-1 by fellow strugglers Burnley in their previous outing at the KC Stadium.
But they were far more resolute against Blues in picking up a rare clean sheet and only their fifth away point of the campaign.
It was all the more meritorious given that Birmingham are unbeaten at home since September and have not been beaten by any of the current top six in front of their own supporters.
Hull remain in the bottom three but will be looking to capitalise on having three of their remaining four games at home if they are to survive the drop.
Dowie clearly decided to try and make the Tigers more difficult to break down in employing only one out-and-out striker and even his most creative midfielder, Jimmy Bullard, was restrained until the latter stages.
Birmingham had made sure of their top-flight status a couple of months ago and there was a lack of intensity about their play as their sequence without a win was extended to seven matches.
Liam Ridgewell got forward to good effect down the left flank and Barry Ferguson was a calming influence in the centre of the park but clear-cut chances were at a premium for both sides, particularly in the second 45 minutes.
Birmingham started in confident fashion and James McFadden cut in from the left and was only just too high with a powerful 20-yard drive.
Scott Dann was proving to be a danger at set-pieces and sent a glancing header just wide from a Craig Gardner free-kick.
Hull threatened for the first time after 16 minutes. George Boateng sent a low ball across the Blues six-yard box after exchanging passes with Bullard and it just eluded Kevin Kilbane at the far post.
McFadden looked sharp and sent over a dangerous cross which Keith Fahey headed back across goal, but Lee Bowyer slipped over when well positioned.
Bullard had one powerful shot blocked by Dann and Keith Fahey had a shot deflected wide before Blues squandered a golden chance after 34 minutes.
Roger Johnson’s cross picked out the unmarked Bowyer but, from six yards out, he sent his header over the bar when the midfielder should have at least hit the target.
Bowyer caused problems to the visitors with his trademark runs and Duke did well to parry away his fierce drive.
Blues enjoyed the bulk of possession but on-loan keeper Joe Hart again proved his worth five minutes before half-time.
Andy Dawson’s overlapping run ended with a cross to the near post and Jan Vennegoor of Hesselink’s header was destined for the far corner of the net until Hart intervened with a fine reflex save.
Barry Ferguson created an opportunity for Jerome early in the second period with a fine through-ball.
The 10-goal striker cut back inside but his eventual shot was easily dealt with by Duke at his near post when McFadden was in space across the other side of the box.
At the other end, Boateng volleyed high and wide when under pressure from McFadden after a Bullard corner was only half-cleared.
McLeish decided a change was required and after an hour he brought on veteran striker Kevin Phillips in place of McFadden.
The former Scotland boss quickly followed up that substitution by taking off Fahey and bringing on Sebastian Larsson.
Blues had strong claims for a penalty rejected when McShane appeared to shove Jerome as he challenged Duke for a high ball from Gardner’s centre.
Dowie made his first change after 76 minutes with Vennegoor of Hesselink making way for Jozy Altidore.
Jerome had a shot deflected wide after Hull failed to deal with a hopeful ball forward from Larsson.
There was rare moment of danger for Birmingham when Bullard broke into the box but his eventual shot lacked power and Hart saved comfortably, before Fagan sent a thumping volley wide in stoppage time.