The Owls Under-18s suffered an opening day 1-0 defeat at Ipswich on Saturday.
There was very little to separate the two sides over the 90 minutes but the game was ultimately settled by a late Elkan Baggott header in Suffolk.
Wednesday so nearly made the perfect start when the lively L’Varn Brandy weaved his way into a shooting position outside the box but drilled just wide.
With very little between the two, the breakthrough almost fell Wednesday’s way five minutes before the interval from a mix-up at the back.
A mis-judged clearance from a Toby Kenyon punt allowed Charles Hagan space to dart into the box and pick out Elliott Vasalo, who spun and shot six yards from goal forcing a good reaction save.
Chances were at a premium in the second half, with the Owls struggling to conjure anything in front of goal, save a Brandy effort inside the box that was comfortably dealt with by goalkeeper Jake Alley.
The decisive moment fell for Town six minutes from time when Baggott arrived at the back post to head home from a Matt Healy free kick.
Wednesday have their first league clash of the season at Middlewood Road on Saturday against Millwall (1.00pm)
Owls: Jackson, Farmer, Ellery, Kenyon, Thompson, Reaney (Cox 63), Hagan, Glover, Vasalo (Bonnington 84), Hall, Brandy (Aguas 76)