The Serbian's close-range effort got Blues out of jail, with the towering striker finishing well after Curtis Davies had flicked on David Murphy's throw. Zigic had earlier given City a ninth-minute lead with a header straight from Murphy's long throw, with his brace taking his tally to four for the season.
The impressive Lee Martin equalised on 18 minutes after finishing a driving run from midfield with a superb strike from 20 yards to register his first goal since the opening day of the season.
Both sides rang the changes after their FA Cup ties at the weekend, Blues recalling seven players and Ipswich five, including a debut for goalkeeper Alex McCarthy following his loan signing from Reading. And there were just nine minutes on the clock when McCarthy was beaten as the hosts took the lead out of nowhere.
Murphy's throw was met by Zigic and the 6ft 8in forward flicked a header backwards which kissed the far post before nestling in the net.
As Blues went in search of a second, Chris Burke's teasing low cross was turned behind by Carlos Edwards with Jean Beausejour waiting to pounce, with Zigic heading the resulting corner into the side-netting.
But Ipswich were soon level with their first meaningful attempt of the game, Martin picking the ball up in midfield and embarking on a strong run before planting the ball left-footed across Boaz Myhill.
McCarthy got down comfortably to another flicked Zigic header from a Murphy free-kick midway through the half, while at the other end Myhill palmed away Town skipper Grant Leadbitter's stinging set-piece from the left channel.
Jason Scotland saw an effort deflected wide for Town while Jonathan Spector failed to find the well-placed Marlon King 12 yards out. Martin was next to see his strike blocked by Davies before Zigic tamely headed a clear opening at McCarthy with the game hanging in the balance.
Blues came closest to regaining the lead in the 73rd minute as King thundered a half-volley against the outside of a post from Burke's cross. Ipswich appeals for a penalty were waved away after Steven Caldwell's tackle on Martin before the late drama settled matters.