Blues head into an uncertain five days as the January transfer window prepares to close, with several big names linked with moves away as they look to raise much-needed funds.
And it was leading scorer Marlon King who snatched victory in the 90th minute when he fired home his 14th and possibly final goal for the side.
Another one of Blues' prized assets had put them in front midway through the first half as Curtis Davies, who contributed with a fine display, converted from Rob Hall's corner.
Arguably the decisive moment of the match arrived just after the hour mark as Dean Marney saw red for lunging in on Paul Robinson.
The dismissal came with play-off chasing Burnley, who were below-par in the first period, in the ascendancy having smashed the bar through Danny Ings and levelled from the penalty spot courtesy of Ross Wallace, coming after Junior Stanislas was brought down by Robinson.
Blues' victory was only their second in nine league games while it ended a three-match winning run for the in-form Clarets.
It was a finely balanced start to proceedings at Turf Moor, where plenty of great work had gone into ensuring the clash got the go-ahead after a host of overnight snow.
Ings twice headed off target from Wallace crosses before Blues broke the deadlock after 21 minutes thanks to Davies, just as he had done in a 2-2 draw between the two sides just before Christmas.
It came courtesy of a familiar double act for Blues fans, on-loan West Ham winger Hall delivering a pin-point corner which Davies met from close range to convert.
Blues, without being spectacular themselves, were comfortable after taking the lead and had little problem holding off a very ordinary first-half display from the hosts.
The Clarets finally threatened in the 40th minute amid a late rally, Chris McCann bringing a save out of Jack Butland after a well-worked move involving the midfielder, Ings and Marney.
Burnley boss Sean Dyche made crucial tactical changes at the break in order to try and inspire his side, rejigging his attacking options.
And it appeared to be just the trick as Ings, Burnley's liveliest outlet, ratted the underside of the crossbar just four minutes after the restart.
Butland was soon called upon to turn Sam Vokes' effort around a post before the home side's pressure paid off in the 54th minute.
Robinson was guilty of bringing down Stanislas in the area and Wallace smashed the resulting penalty down the middle.
Davies headed straight at Lee Grant before Burnley were then reduced to 10 men, Marney dismissed for diving in on Robinson in the middle of the park.
The Clarets initially dominated despite their numerical disadvantage but it was Blues who finished stronger as they applied the pressure, Zigic heading the best chance against the woodwork.
That was until King had the final say in the 90th minute when he fired home from Zigic's header.
Source: DSG