Storey, who was recalled to the side in place of Dominic Iorfa for the trip to the University of Bolton stadium, poked the ball over the line from a second-half corner to give the visitors the lead in front of more than 5,000 ecstatic travelling fans.
But defender MJ Williams fired home from a corner kick at the other end in added time to deny Darren Moore’s side all three points in Lancashire.
Wednesday remain fifth in League One, level on points with the two sides below them.
Scroll down for our player ratings.
5. Sam Hutchinson - 7
Stopped a goalscoring chance with some smart defending in the first period and was one of the Owls' stronger performers. Photo: Steve Ellis
6. Jack Hunt - 6
Teed up Mendez-Laing in the first half for what should have been the opening goal and was his usual energetic self down the right-hand side. Photo: Steve Ellis
7. George Byers - 5
Game seemed to pass him by before he was replaced on the hour mark when Bolton were on top. Photo: Steve Ellis
8. Massimo Luongo - 7
Did the ugly side of things well all afternoon. Perhaps Wednesday's best player on an afternoon when they didn't have things all their own way. Photo: Steve Ellis