A Fernando Forestieri penalty gave Wednesday their second away win of the season, while Huddersfield dropped their first home points.
And it was a well-deserved win for the Owls, who hit the woodwork twice before the game’s defining moment in the second half.
Indeed, they took the game to the high-flying Terriers and might have been ahead inside five minutes.
A concerted bout of pressure saw Kieran Lee and Gary Hooper go close before David Jones struck the crossbar with a teasing cross from the right.
Wednesday continued on the front foot but Huddersfield improved as the contest progressed.
Winger Rajiv Van La Parra was the hosts’ main threat, with a range of eye-catching skills from the left flank.
And it was the former Wolves man who created his side’s best chance of the first half, cutting in to find Nahki Wells but the striker’s shot was smothered by Keiren Westwood.
The Owls’ keeper was called into action moments later, this time saving a Kasey Palmer snapshot from just inside the penalty area.
Wednesday countered, though, and Adam Reach was denied by Chris Lowe just as the midfield man was about to pull the trigger.
Then, just after the restart, Forestieri came within a lick of paint of breaking the deadlock.
The Italian showed terrific skill in pulling a Westwood punt from the sky before executing a clever chip that bounced against the post and back to safety.
Huddersfield hit back with Lowe brushing the top of the net from a set piece – before Wednesday took the lead on 67 minutes.
La Parra handled a Tom Lees shot in the area, the referee pointed to the spot, and Forestieri sent Danny Ward the wrong way from 12 yards.
With the Terriers pressing for an equaliser, gaps appeared for the counter and Gary Hooper almost made the points safe only to be thwarted from underneath the bar by Mark Hudson.
Liam Palmer then rampaged forward into the danger zone but Ward prevented what would have been a rare goal for the defender.
Huddersfield threw everything forward in the final moments but the Owls held firm and advanced to seventh in the table, outside the play-offs only on goal difference.
Wednesday: Westwood, Palmer, Lees, Hutchinson, Pudil, Lee, Jones, Bannan (Wallace 57), Reach, Forestieri (Nuhiu 85) Hooper Loovens 90)