A Gary Gardner own goal and Lewis O’Brien’s strike gave Carlos Corberan’s side a two-goal advantage at half-time and it was enough to move up to third in the table.
Juninho Bacuna and Onel Hernandez hit the woodwork for Birmingham in an improved second-half performance, but ultimately the Terriers were able to make it three straight wins fairly comfortably and 31 points from their last 45 available.
Birmingham, who lost striker Lyle Taylor to injury in the warm-up, saw makeshift centre back Maxime Colin depart to a knock in the 25th minute.
Jordan James was promoted from the bench while Ivan Sunjic came on for Colin, which forced captain Gardner into the back four.
Huddersfield took a 27th-minute lead with the first serious attack.
Poor Birmingham defending allowed Sorba Thomas’ inswinging corner to find on-loan Chelsea defender Levi Colwill to chest the ball at the far post and it went in off Gardner.
It was a timely birthday present for Colwill, who turned 19 today.
The goal livened proceedings up, and there were chances at both ends as the game opened up.
Perhaps not surprisingly given their form, Huddersfield had more of the play and looked more menacing.
Huddersfield midfielder Lewis O’Brien saw a first-time angled shot saved by goalkeeper Neil Etheridge, who was then smartly off his line to deny a clean-through Jordan Rhodes.
Blues’ first opportunity came in the 32nd minute when Hernandez produced a snapshot that hit goalkeeper Lee Nicholls and went out for a corner.
The home side were looking increasingly vulnerable at the back and Duane Holmes was left clean through only to blaze high and wide.
O’Brien made it 2-0 in the 44th minute after more catastrophic Blues defending.
Gardner allowed a pass to drop over his head then could only make a real hash of his clearance across his own box, where Jeremie Bela slid in but could not keep out O’Brien, who side-footed home.
Birmingham improved after the break but found Huddersfield’s defence and Nicholls in particular tough nuts to crack.
The lively Hernandez cut inside before driving just wide and Ryan Woods saw a shot from the edge of the box deflected off target, then Bacuna’s curling shot was tipped against the post by Nicholls.
Sandwiched in between was an angled drive from Thomas which hit the outside of the Birmingham upright.
But Blues were next to hit the woodwork when another shot from Hernandez was helped on to the bar by Nicholls.
Blues’ attacking petered out however and Huddersfield were able to complete a comfortable victory.