The Villans were unable to find a way through from their 14 attempts on enemy territory, twice hitting the bar in the second half, but the point is enough to keep them in the Championship's top six.
Birmingham, now winless in 11 derby meetings against Villa, move up to 12 points for the season after winning one, losing one and now drawing one of their first three games under boss Steve Cotterill.
Glenn Whelan sent a deflected shot narrowly wide soon after as the visitors took control of proceedings in the opening quarter of a feisty affair, which sparked into life when Robert Snodgrass grabbed Che Adams - both players seeing yellow.
Johnstone was almost at fault for a breakthrough goal before the interval, though, as his attempted punt came back off Isaac Vassell and flew inches wide of the target.
Chances also came and went for Cheikh N'Doye and Jota either side of the half-time break, the latter failing to keep his composure when nipping in to intercept a Conor Hourihane pass and finding himself through on goal.
Birmingham just could not put the ball in the net and, after Sam Gallagher steered over the bar, Villa nearly punished their opponents through a Kodjia near-miss.
Kuszczak was being worked a little more as the game headed into the final 30 minutes, keeping out a Kodjia header and then seeing John Terry nudge narrowly wide.
Villa will feel aggrieved not to have snatched all three points as Keinan Davis and Kodjia both picked out the frame of the goal in quick succession, which proved to be the closest either side came to winning it.