David Wagner's charges began the game with an intensive press and they soon took control of the encounter in typical Huddersfield style with a number of neat possessional interchanges, only to see the visitors hold firm at the back.
With chances hard to come by in the opening half, the Terriers might have found an influential lead through Isaiah Brown, as the youngster reacted quickest in the box to produce a half-volley that clipped the top of Keiren Westwood's crossbar.
The Owls continued to sit deep in order to frustrate the home side and they were able to see out the remainder of the first period without conceding, despite Town holding a large share of possession.
Huddersfield went about their second-half business in much the same way as their first and they could have gone in front when Nahki Wells sought to lob Westwood from the edge of the area, leaving the stopper to scramble back and tip the effort over his bar.
The home side's dominance continued and they had another chance to earn a vital lead in the playoff, but Wells was again thwarted by Westwood, who rushed off his line to deflect the striker's effort wide of the target after a scramble inside the box.
With proceedings heading towards a draw, Wednesday introduced Jordan Rhodes up top but the striker was unable to change the course of the game as things remained level heading into the return fixture at Hillsborough.
Town suffered a late scare with six minutes remaining when Barry Bannan broke clear on the edge of the area, but the midfielder's speculative effort flew just a few inches too high of the hosts' goal, leaving the game ending goalless.