In a game of few chances, Wigan were handed a lifeline on the hour mark when the on-loan Manchester United striker was given a straight red from referee Stephen Martin for a lunge on Jordi Gomez.
But Blues held on for a point that extends their unbeaten run to eight matches.
The closest either side came to a goal was just before the break when Callum McManaman surged through, only to see his left-foot shot well saved by Darren Randolph.
Wigan had gone into the game without star man Nick Powell and they struggled to assert themselves from the off.
The visitors, in their best run of form of the campaign, looked far more livelier in the opening stages.
Nikola Zigic saw a header well collected by Ali Al Habsi before Chris Burke fired wide of the target.
Burke was seeing plenty of the ball early on and his cross was steered just wide by Lingard.
Thomas Rogne had to be on hand to block a goalbound strike from Lee Novak, with another Burke delivery flying just in front of Tom Adeyemi.
Wigan played themselves into trouble when Chris McCann put Al Habsi under pressure but Burke's subsequent cross came to nothing.
The FA Cup holders were forced into an early change when Ryan Shotton took over from the injured Rogne, and they were claiming a penalty when Dan Burn was all over James McClean.
More clever feet from Burke resulted in his shot being blocked by Leon Barnett before Wigan nearly found a goal against the run of play at the end of the half.
McManaman did all the work himself, racing through and seeing his shot tipped round the post by Randolph.
Wigan made their second change at the interval, Gomez for McClean, and they were again screaming for a penalty when Holt appeared to be bundled over by Randolph.
Birmingham sent on Andrew Shinnie for Burke, a surprising move given the winger's involvement up to that point.
And his departure coincided with Wigan coming more into the game.
Clever play from Gomez twice threatened to open the door, James Perch having a shot blocked and Shotton drilling wide of the far post.
The flashpoint then came on the hour mark, resulting in Birmingham playing out the game a man light.
The visitors thought they should have received a free-kick when McCann brought down a breaking Lingard.
Referee Martin waved play on, though, and Lingard showed his displeasure by immediately going in on Gomez and sparking a melee that involved most of the players.
Lingard was given a straight red for his troubles, which gave Wigan renewed heart heading into the final third.
Perch's cross was flicked on by James McArthur, only for Gomez to mis-kick.
And Jean Beausejour's cross was stabbed just wide by James McArthur at the near post.
Wigan made their final change when Manchester United loanee Will Keane took over from McCann.
But the home side could not make their numerical advantage count as their front three failed to click.
They were claiming another penalty in the fourth added minute when Beausejour went down inside the box, but again the official waved it away.