Wolves boss Mick McCarthy claimed before the game that he was dealing with the worst injury crisis he has experienced in almost two decades of management, but his makeshift side did him proud.
The home side were on the front froot from the very first whistle against their West Midlands rivals and Hunt's goal, a near-post finish from Sylvan Ebanks-Blake's cross, came after Ben Foster had already made two excellent saves.
Wolves missed further chances after the break and were nearly made to pay by their old foe Kevin Phillips, who headed wide when unmarked after coming on as a substitute.
McCarthy's men held on, though, to record their first clean sheet since April and move to within a point of Wigan and Fulham above them. Blues are now just three points away.
With enough players sidelined to make an entire starting XI, McCarthy was forced to make four changes from the side who went down 3-0 at Blackburn last weekend - Kevin Doyle (dead leg), Matt Jarvis, Michael Mancienne (both knee) and Steven Mouyokolo (back) making way for Ebanks-Blake, Hunt, David Edwards and Richard Stearman.
Birmingham counterpart Alex McLeish also made three changes, handing starts to Serbia striker Nikola Zigic, Sebastian Larsson and David Murphy.
The opening stages were played at a typical bustling derby tempo, setting the trend for the afternoon.
Foster's first save of the encounter came with 10 minutes on the clock, diving to his right to pluck Edwards' goalbound header out of the air.
The former Manchester United stopper was at it again less than 60 seconds later, denying Hunt with a great point-blank block after the ball broke six yards out.
Blues were losing possession far too easily in the final third, meaning they were struggling to create a worthwhile chance.
Foster was made to work again just before the half-hour mark, getting down low to save Ebanks-Blake's shot on the turn from the edge of the area.
Wolves, despite their injury crisis, were definitely looking the most likely to break the deadlock.
Stephen Ward lobbed a speculative effort over the crossbar before Ebanks-Blake was again left cursing the form of Foster as he parried his drilled effort at the near post.
Ward did find the net just before the interval but he was rightfully flagged offside.
Yet there was nothing wrong with Hunt's 45th-minute breakthrough as he got in between Roger Johnson and Stephen Carr to connect with Ebanks-Blake's low cross, leaving Foster with no chance.
The lively Edwards should have doubled Wolves' advantage within minutes of the restart, somehow planting his unmarked header inches wide from Ward's right-wing cross.
The momentum from the first half had failed to shift and Foster was again called into action, getting his body behind Nenad Milijas' free-kick before collecting Ronald Zubar's tame shot.
Christophe Berra headed over from Hunt's corner as McCarthy's side looked for a killer second.
Birmingham were in desperate need of some fresh impetus and McLeish turned to Craig Gardner and Jean Beausejour from the bench.
But it was Foster who continued to be the visitors' key performer as he produced his umpteenth save of the match to tip Milijas' header over the bar.
Berra collided with a post as he tried to head home, but Wolves were unable to build on their one-goal advantage with 20 minutes remaining.
Ward's dangerous cross was well held by Foster before McLeish threw his last roll of the dice, bringing on former West Brom man Phillips to boos from the Molineux faithful.
Despite the home side's dominance they nearly threw the points away as the game entered the final 15 minutes but Cameron Jerome was unable to connect with Beausejour's left-wing cross when, if he had, he surely would have scored.
Phillips, who has a wonderful record in derbies, had an even better chance in the 89th minute but got his angles all wrong and headed off target, much to the relief of the majority of the 25,150 present.