The Owls made three changes from the team which lost last time out at Charlton.
In came Jeremy Helan and Jose Semedo for midfield duo Barry Bannan (injury) and Sam Hutchinson (banned), while Atdhe Nuhiu replaced on-loan Gary Hooper up front.
For Town, Nahki Wells led the attack in David Wagner's first game in charge.
The first 45 minutes offered few chances, littered with niggling fouls from both sides.
Fernando Forestieri went close for the Owls with a header, while home goalkeeper Keiren Westwood blocked Kyle Dempsey's effort with his legs.
But Sean Scannell headed home, from Kyle Dempsey's cross, after the break to put Town in front.
Ross Wallace went close to a swift equaliser, but his long-range effort was blocked.
With Lucas Joao, Lewis McGugan and Gary Hooper all coming on as second-half substitutes, the Owls were pushing for a goal.
And two arrived, as first Joao pounced to level before Forestieri played in Kieran Lee for the second.
As Town pushed for an equaliser, Joao raced away to curl the ball beyond a stranded Joe Murphy.
Owls head coach Carlos Carvalhal said: "I think we deserved to win the game. We showed that we have a strong team. The strong teams can do what we did today.
"It was not good in the first half but we were better in the second half. We started very well in the second half and after Huddersfield scored, it was a fantastic reaction.
"The energy we put on the pitch was very difficult for Huddersfield.
"We won because of fantastic teamwork. All the players played their part. We win with the team and not with individual players.
"Fernando (Forestieri) is a player who works a lot for the team and it is important to me that players fight for the team.
"We know that Lucas (Joao) can give us a lot of pace and energy and he provided that when he came on.
"We must only talk about game by game and the most important game is the next one.
New Huddersfield head coach David Wagner, who took charge of the side for the first time, said: "All over the world, the result is the important thing and this is why we are disappointed.
"In the last 20 minutes, we have to be honest and say that Sheffield Wednesday were very strong. In that time they beat us.
"The first 70 minutes was a step in the right direction. We needed a better performance in the last 20 minutes.
"There were a lot of good moments for us in the game. We had very good transition moments and I think we defended well for a long time.
"After their second goal, we tried to play long balls in the hope of getting a second goal, but it didn't work.
"We need a higher level in our fitness and there was a lot of information we can work on.
"We like to create a new style and for this you need unbelievably good fitness. That is what we are working towards."
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