A terrific first-half display, with goals from Paul Anderson and Daryl Murphy, paved the way for a crucial win that puts Town firmly back in the Play-Off race.
Blues could have scored twice before Anderson found the net with a superb strike on six minutes.
Jonny Williams, again prominent in everything good about Town as an attacking threat, was close to adding a second before Murphy grabbed his 11th goal of the season to put Mick McCarthy’s side in control of a game they rarely looked like letting slip.
Town made two changes to the side that went down at Blackburn at the weekend, Anderson and Stephen Hunt coming in, with Anthony Wordsworth and Frank Nouble dropping to the bench.
Anderson was immediately in the action, stabbing the ball goalwards from Murphy’s cross that brought a smart save from Alex Smithies.
Williams then had a gilt edged chance to open the scoring when Hunt fed the Crystal Palace loanee with a great flick but Smithies came to his side’s rescue again.
Town would not be denied though and a minute later, Anderson cut in from the right and curled a beauty with his left foot into the Terriers’ net.
Blues swarmed all over the home side and Murphy led a four man break, his cross cannoning back off Anthony Gerrard and then to safety.
Nahki Wells fired over as Huddersfield looked to get a foothold in the game but it was Blues who were flowing forward at every opportunity, Cole Skuse splitting the home defence with a terrific pass and Williams sending a 25 yard screamer over the bar.
Williams’ cross was then headed out by Joel Lynch as Murphy threatened at the far post then Luke Chambers looked certain to score with a close range effort but the ball deflected off a defender and drifted just over the bar.
Dean Gerken punched clear from Adam Hammill’s cross, Adam Clayton picking up the loose ball 30 yards out but smashing it high and wide.
Murphy left the Terriers’ defence for dead when he burst clear down the right but his cross-cum-shot flashed across goal, then Anderson was denied by Smithies when clean in on goal after Williams had gone down under a challenge inside the box.
Blues got the second goal that had been coming though on 33 minutes, Murphy jabbing the ball past Smithies from just inside the box to take a stranglehold on the game.
Williams had another effort at Smithies, the home team rocked back by the fluent Town passing, Anderson then inches away from getting on the end of Chambers’ cross.
Neat play by Wells conjured up a chance for Danny Ward at the other end but he couldn’t direct the cross goalwards, Gerken then off his line quickly to clear the danger after Wells looked to get on the end of a long ball as the first-half came to an end with Town in control of the game and probably deserving to be further ahead than just the two goals.
Huddersfield made a change before the second-half got underway, with Sean Scannell on for Hammill.
The influential Anderson sent a left foot curler wide after Murphy led a breakaway, Blues starting off on the front foot again before Duane Holmes joined the action with Oliver Norwood making way.
Town were forced into a change on the hour with Aaron Cresswell limping off, Tyrone Mings his replacement, the substitute making a timely interception from Holmes with his first touch.
Hunt over-hit a free-kick after Williams had been sent crashing to the ground on the edge of the box, the Huddersfield defence struggling to deal with his pace and movement.
Anderson darted in on the blind side to get on the end of Murphy’s cross and force Smithies into a save as Blues looked to close the game out, Ward hooking the ball over the bar at the other end as the Terriers looked for a way back into the game as the clock ticked around to 70 minutes.
Hunt, who picked up a yellow card for dissent, was replaced by Wordsworth, Harry Bunn on for Ward in Huddersfield’s final change.
Gerken preserved Town’s lead with a vital save with his feet from Oscar Gobern 10 minutes from time in Huddersfield’s best chance of the game.
Frazer Richardson was introduced for the final exchanges as extra insurance for Blues, replacing Williams as Town eased to the win and closed that gap on the top six to just two points.