Two goals from Jonathan Kodjia were not enough to inspire City to victory in an entertaining affair at St Andrew’s.
The Frenchman twice reduced the home side’s lead to a single goal, but Clayton Donaldson’s first-half hat-trick always left the visitors playing catch up, before Jonathan Grounds headed Birmingham’s fourth 12 minutes from time to effectively end City’s hopes of salvaging a result.
Steve Cotterill made four changes to his side and handed debuts to both of his deadline day loan signings, as Aden Flint was flanked by Liam Moore and Nathan Baker in a new-look City back three.
Elsewhere, Cotterill was able to welcome Frank Fielding and Luke Freeman back from injury and suspension respectively, with Ben Hamer, Derrick Williams, Mark Little and Bobby Reid dropping to the bench.
But it would prove a difficult transition for the new faces, as teenage livewire Demarai Gray escaped down the City left and crossed deep towards David Cotterill, who slid in to turn the ball back across goal for Donaldson to convert with a simple tap-in.
City looked confident enough going forward, with Freeman breaking from midfield on a couple of occasions inside the first 20 minutes, but shooting opportunities were not forthcoming.
The most presentable opening fell the way of the front two when Aaron Wilbraham latched on to Luke Ayling’s ball over the top, but elected to find strike partner Kodjia whose first touch was snuffed out.
It was clear that Birmingham possessed some talented individuals, with Gray giving Moore a tough time down the Blues left and Jon Toral providing a creative spark behind goalscorer Donaldson.
It was the Spaniard on loan from Arsenal who showed his ability to unlock the City defence with an eye of a needle pass to find Donaldson in plenty of space to score from what looked an offside position – though with defenders stepping up looks can be deceiving.
Another half-chance fell City’s way when Freeman’s delicate chip forward picked out Kodjia, only for the Frenchman to mistime his volley and barely make contact from 15 yards.
Birmingham had their tails up and should have been out of sight when Toral headed a Cotterill corner wide from virtually point-blank range, while Donaldson seemed to be impeded by Flint in the box but received no sympathy from referee Mark Brown.
Instead City threw themselves a lifeline on 32 minutes with a well-worked goal.
Ayling, operating at right wing-back, drifted all the way towards the left corner of the penalty area before sliding the ball inside the full-back for Joe Bryan, whose delicious low cross was converted from six yards by the sliding Kodjia.
Suddenly it was the visitors with their tails up at the end of a gripping first half, and Marlon Pack had Tomasz Kuszczak scrambling in vain when his curling free kick struck the keeper’s left-hand post soon after.
But instead City would have a mountain to climb at the start of the second period, as Toral danced his way into the box before he was supposedly impeded by an arm across the chest from Wilbraham, who pleaded his case only for Donaldson to complete his hat-trick with the coolest of penalties.
City had shown enough to suggest they could still find a way back into the game, but only by preventing any further damage at the other end.
It would take Flint to throw his body on the line to keep out Donaldson when he turned in the box after Moore had poleaxed Toral in the build-up and received a booking for his troubles.
But it was a relatively isolated moment of concern as City began to take control of the second half.
Wilbraham laid the ball back for Pack to place a 20-yard shot inches wide – a shot the midfielder was convinced took a deflection on its way past the post.
Cotterill opted to switch to an orthodox 4-4-2 formation just after the hour, as Williams replaced the carded Moore to play at left-back and Callum Robinson operated from the right wing in place of Pack.
Robinson was immediately involved in rushing to meet Bryan’s low cross that only needed a touch but seemed to fizz beyond the substitute fractionally too quickly.
However, City were soon back to within one goal when Kodjia struck again to register his fourth goal of the season, brilliantly volleying home Flint’s hooked ball back across goal from ten yards.
But another ray of hope was cast into the shadows in the space of 12 minutes, as Grounds headed Cotterill’s corner down past Fielding’s left hand, before Flint sliced wide from a presentable chance that needed to be taken to spark a late revival.