On-loan Barcelona midfielder Hleb, making his St Andrew's debut, broke the deadlock in the 24th minute and he was soon joined in bagging his first goal for the club by summer signing Zigic.
And just four minutes after taking the lead the hosts had established a commanding three-goal advantage as Gardner lashed into the bottom corner from 25 yards.
Dons, fourth in npower League One, deservedly bagged a late consolation through substitute Aaron Wilbraham - but were completely unravelled by the devastating four-minute spell in what was the first meeting between the two sides since the club's 2004 relaunch.
It is also the first time Alex McLeish has guided Birmingham into the fourth round of the competition and he will now have one eye on Saturday's draw with a strong cup run a real possibility based on the strong squad at his disposal.
As promised, the Blues boss made a raft of changes to the side which lost 3-1 at West Brom on Saturday.
Summer signings Zigic, Matt Derbyshire, Jean Beausejour and Martin Jiranek were all handed starts, with the latter two making their full debuts, as part of nine new faces.
Only Hleb and new captain Roger Johnson remained.
MK Dons boss Karl Robinson made just one switch from the XI which drew 1-1 at home to Rochdale, Mark Carrington coming in for Jabo Ibehre who dropped to the bench.
Robinson vowed not to change the Dons' passing style for the tie and the visitors certainly looked comfortable on the ball in the early exchanges.
But it was Zigic who should have opened the scoring for Blues after just eight minutes. The ball broke kindly for him in the middle of the penalty area but he waited far too long and was eventually escorted away from goal.
McLeish was struck a blow in the 23rd minute when Michel was forced off with an injury having pulled up, with Gardner replacing the Spaniard.
But the Blues boss was all smiles within 60 seconds as Gardner found Beausejour on the left. He fed Hleb on the edge of area and he had plenty of time to pick his spot.
Within two minutes it was 2-0. Beausejour was again the architect, looping a ball into the path of Zigic, who showed cool composure under pressure to nick the ball past David Martin.
And before the visitors could catch their breath, Gardner had rifled in a low third from distance to all but seal the tie.
The League One side certainly had their chances as they looked to snatch a goal before the break. Oncoming substitute Ibehre saw an effort well blocked, Dean Lewington twice headed over and Lewis Guy stung the palms of goalkeeper Maik Taylor.
The visitors had not quite thrown in the towel in the second half but the odds were against them clawing back a 3-0 deficit against a side unbeaten at home in nearly a full year.
However, that did not stop them going in search of a consolation as Taylor saved from Carrington and Guy.
Centre-back Jiranek sidefooted over the bar when unmarked in a good position before Zigic headed wide from Stuart Parnaby's deep cross as Blues went in search of another.
But the visitors who grabbed the fourth goal of the night in the 80th minute, Wilbraham capitalising on a mix-up in the home defensive to lash past Taylor and into the bottom corner.
Dons pressed in search of a quick second as the majority of the 9,450 crowd inside St Andrew's became edgy, but there was no pulsating finish.