Blues had gone behind in 15 of their previous 22 npower Championship matches before the contest but it was they, fielding seven teenagers in their starting XI, who took the lead after half an hour 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.