In a top-of-the-table clash at the League One summit, Wrexham had a ninth-minute lead. Ollie Palmer forced a turnover high up the pitch and Ollie Rathbone curled an exceptional 20-yard effort into the top corner.
But Birmingham had an equaliser by the 20th minute, as Lyndon Dykes found himself free in the box and headed through a crowd.
The game seemed to descend into a stodgy midfield battle thereafter, but James McClean came close on the hour, forcing an excellent save from Ryan Allsop with a close-range header from a corner.
On the 68th minute, Wrexham rang the changes and introduced both Paul Mullin and Steven Fletcher, for Palmer and Elliott Lee, as they attempted to twist, instead of sticking.
It was to no avail, as the two sides huffed and puffed, but were unable to find the required quality to win the game.
Birmingham subsequently stay top of the table, with Wrexham in third.