The home side made a fine start as David Cotterill fired them ahead after 10 minutes, rounding the goalkeeper and tucking the ball into the net from six yards.
Huddersfield striker Harry Bunn, who recovered from a hamstring injury to start the game, lasted just 20 minutes before he was replaced by Sean Scannell, and the substitute should have equalised within 20 seconds of coming on, but he put an effort wide from close range.
Both sides then went close to taking the lead as Huddersfield keeper Alex Smithies tipped Andrew Shinnie's header over the bar, before Lolley missed an effort at the back post from Scannell's low cross.
Smithies then tipped a powerful long-range effort from Paul Caddis over the bar as Birmingham grew in confidence, and they then had three glorious opportunities to score, but Wes Thomas had a shot cleared off the line and Rob Kiernan had two efforts saved.
Neither side could find a winner and were forced to settle for a point.