The beanpole Serbian striker cancelled out Leeds striker Ross McCormack's 19th-minute opener with a first-half header and struck three times in seven minutes in the second period as Chris Hughton's rampant Blues ran riot.
Leeds fans, who saw their side beaten 5-1 at Elland Road by Blackpool in November, turned on chairman Ken Bates soon after Zigic headed home his fourth in the 68th minute.
He was forced off after landing awkwardly, but the damage was done as Blues extended their unbeaten run to 10 matches.
Luciano Becchio and defender Aidan White returned for Leeds, but there was no place in the squad for deadline day loan signing Adam Smith, from Tottenham, while another recent recruit, USA international Robbie Rogers, was not included.
Blues, beaten only once since exiting the Europa League in December, made three changes, with goalkeeper Boaz Myhill, midfielder Keith Fahey and Zigic recalled.
Leeds twice threatened to take the lead in only the second minute when Becchio's goalbound header and then McCormack's shot were both blocked on the goalline.
Becchio then wasted another golden chance to give Leeds a flying start, sidefooting wide with just keeper Boaz Myhill to beat after being played through by McCormack.
But McCormack gave the Elland Road crowd a huge lift in the 19th minute when skipping too easily past Blues defender Curtis Davies and arrowing a left-footed shot into the bottom corner.
Leeds' hard work was undone by a soft equaliser in the 31st minute.
Wade Elliott was afforded too much space to cross from the left and Zigic slipped his marker to steer home an easy header.
Becchio was denied a spectacular goal from 30 yards only by Myhill's acrobatics in the 57th minute.
But just as Leeds began to force the issue Zigic blasted Blues into a 61st-minute lead.
Chris Burke raced on to a crossfield pass and turned left-back White inside out before cutting the ball back for Zigic to fire high into the net.
Three minutes later the Serb headed home his hat-trick. Morgaro Gomis crossed from the left after another swift passing move and Zigic was free to regally head home Blues' third goal.
Elliott forced Andy Lonergan into a fine save with a header as the Blues smelt blood and from the resulting corner Zigic rose highest to power home his fourth and all but seal another win for Hughton's rampant side.
Zigic fell awkwardly and left the field to tumultuous applause from the travelling Blues fans.
The Elland Road kop turned on chairman Bates and the visiting supporters chanted: 'You're getting sacked in the morning' to dejected manager Simon Grayson as Leeds' season appears to be fading fast.