The first action of the game occurred inside a minute as the Terriers took the lead through Joe Lolley, who tucked the ball into the back of the net after some excellent play from Sean Scannell on the right of the pitch.
Blues winger Demarai Gray then produced a save from Jed Steer as the home side searched for an equaliser, minutes before Nicolai Brock-Madsen failed to convert a great chance from a David Davis cross.
Birmingham claimed for a penalty just under 15 minutes before the half-time break when Jonathan Grounds was pushed to the floor, but the referee was quick to deny the opportunity of a spot kick.
Lolley had a chance to double Huddersfield's lead, but his effort was deflected just wide on the stroke of half time.
The break was followed by a quiet second half, with a wide shot from Huddersfield's Emyr Huws one of very few chances before the final 10 minutes.
The result moves Huddersfield up to 19th, now two points above the relegation zone, while Birmingham drop out of the Championship playoff places into seventh.