The Saddlers looked capable of getting the result they needed when they took the lead after just 10 minutes, veteran striker Jon Macken driving in his ninth goal of the season when Julian Gray's cross bounced off Richard Taundry into his path.
Dean Smith's side were fighting for every ball, with most of the 2,072 present cheering them on, but the Owls soon equalised in the 26th minute
Impressive full-back Lewis Buxton joined up to support the attack and hit a fierce low drive which Walsall keeper James Walker managed to block but he could not hang on to the ball and Neil Mellor tucked away his 18th of the season.
In the second half it was end-to-end stuff with Wednesday looking more likely to score as winger Gary Teale provided a string of crosses and Buxton saw another drive turned round a post by the busy Walker.
Walsall wasted several corners which they should have done better with, and Jordan Cook fired just over following good work by Marc Laird. But the Owls should have scored after 71 minutes when, from Teale's teasing free-kick, big striker Gary Madine met the ball six yards from goal with a downward header which bounced over the bar.