Blues had gone behind in 15 of their previous 22 npower Championship matches before this match but it was they, fielding seven teenagers in their starting XI, who took the lead on the half-hour mark courtesy of Curtis Davies' header.
A contentious moment arrived just before the hour as Charlie Austin saw a goal chalked off when advantage could and should really have been played, but Burnley deservedly got their rewards soon after with two goals in three minutes.
Danny Ings levelled with a well-taken finish before almost straight from kick-off Ross Wallace, also with his first goal of the season, converted a stunning free-kick off the underside of the crossbar.
But Serbian striker Zigic popped up to hammer home his second goal in as many games late on.
It ensured a point apiece for two struggling sides, who have now won just one of their last eight respectively.
Blues manager Lee Clark was hampered severely by injury and suspension, most notably the loss of 13-goal top scorer Marlon King.
And matters went from bad to worse in the build-up to kick-off as he lost the services of Peter Lovenkrands, Nathan Redmond stepping in.
Blues' naivety was showing in the opening stages as Martin Paterson wasted two great chances.
Ings and Chris McCann both threatened before Paterson was then presented with his third clear-cut opening within the first 12 minutes but was denied by a super stop from Jack Butland, with Blues' young full-backs struggling to cope.
But Blues got a grip on proceedings after their early struggles and it was they who took the lead with 30 minutes on the clock.
Joseph Mills was lucky to escape with a yellow card for his foul on Robert Hall on the right wing, and from the resulting free-kick Hall delivered a great cross which was headed home by Davies.
Michael Duff should have levelled for Burnley in the 38th minute but he could only fire over the bar from close range after Butland had parried Dean Marney's header.
Lee Grant then saved twice from Redmond and Hall before half-time.
Redmond again threatened at the start of the second period but it was Burnley who, largely, dominated.
A moment of controversy arrived in the 57th minute as Austin headed home Kieran Trippier's right-wing cross, but play had been halted for a late foul on Trippier by Mitch Hancox, with referee Eddie Ilderton not playing the advantage.
Burnley, however, did not have to wait long for their leveller as they deservedly equalised through Ings, who took a great touch before firing home from close range.
And no sooner had they levelled than the visitors took the lead.
Blues lost the ball straight from kick-off, Davies conceded a free-kick on the edge of the area and Wallace converted a stunning set-piece.
Blues applied plenty of late pressure in search of an equaliser and it finally came in the 89th minute as Zigic blasted home from 12 yards.