The Owls went into the League One game on the back of two straight defeats and it looked like they were going to make it an unwanted hat-trick when they went 2-0 down to the Robins.
After a goalless first half, the home side took the lead with a two-goal salvo shortly after the hour.
Aidan Keena scored his second goal in two games to break the deadlock on 62 minutes and the ever-reliable Alfie May gobbled up a rebound seven minutes later.
However, Wednesday refused to throw in the towel.
Defender Aden Flint headed in a fine cross from Barry Bannan to halve the deficit in the 76th minute before Lee Gregory rescued a valuable point from close range with three minutes left.
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