Not for the first time this season at Hillsborough, the Owls dominated their opponents but had to settle for a share of the spoils.
Huddersfield spent most of the game camped in their own half but Wednesday could not capitalise, despite going ahead four minutes from the end through substitute Sergiu Bus.
But the Terriers had their own threat from the bench in Ishmael Miller, who drew the visitors level at the death.
The home side, however, dominated almost from first whistle to last, although the Terriers had one effort hacked off the line in the first half, a fate that befell the Owls after the break.
Earlier, Wednesday had a spring in their step, with Marnick Vermijl unfortunate to see a clever low cross evade three of his onrushing team mates.
Caolan Lavery then whistled a fierce half volley over the bar before Lewis McGugan poked just wide following a neat three-man move.
For their part, Huddersfield struggled to make a real impression in the final third and the Wednesday goal remained untroubled until 30 minutes in when Joel Lynch sent in a low drive that Keiren Westwood gathered.
But the Owls had an escape four minutes before the interval as the ball fell kindly for David Edgar from a corner but the Town defender saw his shot cleared off the line by the alert Vermijl.
The game needed a lift for the second half and got it on 50 minutes when Atdhe Nuhiu seemed certain to score after outwitting Huddersfield keeper Alex Smithies only to see Joel Lynch cover and clear right at the last.
The Owls pressed on and Lavery hit over after an outrageous piece of skill pulling a Lewis McGugan cross out of the air in the box.
Stuart Gray made a double change just after the hour, introducing Stevie May and the returning Bus, who featured for the first time in two months.
The latter had a chance to make a swift impression after finding space in the area but couldn’t get enough purchase and Smithies saved comfortably.
That seemed to be the story of the afternoon for the Owls, until Bus converted from close range on 86 minutes at the second attempt.
And that appeared to be enough to collect what would have been a merited win but Miller popped up at the death to deliver a late, late blow that sealed a point for Town.
Owls: Westwood, Mattock, Hutchinson, Nuhiu (Bus 63), Lavery (Maguire 74), Lees, Zayatte, Lee (May 63), Isgrove, Vermijl, McGugan
Huddersfield: Smithies, Edgar, James, Hudson, Scannell, Butterfield, Vaughan, Grady, Wells (Miller 65), Smith, Lynch