Oliver Norwood opened the scoring for Town after 16 minutes when he converted the rebound after initially missing from the penalty spot.
Huddersfield were quickly two ahead through Lee Novak, who scored his first goal of the season with a header.
Wednesday reduced the deficit before the break with a header of their own, scored by Reda Johnson.
A frantic match produced red cards either side of the break, when Joel Lynch and Joe Mattock were both dismissed, reducing each side to ten men.
Simon Grayson's side finally made the game safe 20 minutes from the end when they were awarded a second penalty kick.
Adam Clayton took over the responsibility and made no mistake to move Huddersfield into the playoff places at this early stage of the season.