It was a deserved third league win of the season for Simon Grayson's side, who took the lead through Oliver Norwood when he followed up his first-half penalty that goalkeeper Chris Kirkland had saved.
Lee Novak headed home Town's second two minutes later and although Wednesday defender Reda Johnson headed home before the break, Adam Clayton converted another controversial penalty in the 71st minute to condemn Dave Jones' men to a third straight defeat.
Huddersfield defender Joel Lynch was shown a straight red card for his flying first-half lunge on Michail Antonio and Wednesday right-back Joe Mattock was dismissed on the stroke of half-time for a second yellow card as a rip-roaring derby threatened to combust.
Both sides were wearing black armbands and supporters were asked to stand for a minute's silence prior to kick-off in memory of the Hillsborough disaster and two soldiers from the Yorkshire Regiment who were killed last week in Afghanistan.
After a busy start to the game it was the visitors who took the lead in the 16th minute.
Huddersfield right-back Jack Hunt was tripped by flat-footed Owls winger Jermaine Johnson in the penalty area, leaving referee Graham Salisbury no option other than to point to the spot. Norwood's penalty was saved by Kirkland, but the midfielder followed up to steer home the rebound.
Huddersfield doubled their lead two minutes later. Winger Danny Ward lost his man thanks to Paul Dixon's decoy run to deliver an inch-perfect cross from the left and an unmarked Novak headed into the top corner.
Wednesday pressure paid off when they pulled a goal back in the 37th minute.
Antonio's long throw was headed on by Jay Bothroyd and Reda Johnson headed home at the far post.
Huddersfield were reduced to 10 men in the 38th minute when Lynch was shown a straight red card for his scything tackle on the elusive Antonio.
Town manager Simon Grayson, who protested furiously, sacrificed Novak for substitute Anthony Gerrard a minute later and the former Cardiff defender was duly booked for entering the field without referee Salisbury's permission.
Wednesday defender Mattock, booked for unsporting behaviour shortly after Lynch's dismissal, was then shown a second yellow card for his foul on Ward to even things up on the stroke of half-time.
Both sides engaged in keep-ball after the restart, but urged on by increasingly impatient fans, the home side began to show more urgency and Reda Johnson headed a good chance off target.
Wednesday substitute Nejc Pecnik, on for Gary Madine, then rolled a shot agonisingly wide.
But Town were awarded a controversial second penalty. James Vaughan's cross appeared to hit substitute Rhys McCabe on the hand and even though referee Salisbury was unimpressed, his assistant Barry Gordon vigorously waved his flag and following consultation the spot-kick was given.
This time Clayton stepped forward and planted his penalty into Kirkland's bottom right-hand corner to restore the visitors' two-goal advantage.
Reda Johnson spurned a golden chance in the 82nd minute when he somehow directed Antonio's cross wide, but although the home side pressed for a second goal, Huddersfield held firm for their first away win of the season.