Wednesday had to survive some first-half pressure but they never looked back after David Prutton's high-class opening goal.
Oldham went close through Dean Furman's early drive and they should have gone in front when Shefki Kuqi headed a good chance over the bar.
Wednesday's Ben Marshall floated a free-kick just off target, but Oldham threatened again as Robbie Simpson forced Stephen Bywater to save well.
Owls sub Ryan Lowe's effort was kept out by Oldham keeper Alex Cisak, but Gary Megson's side went ahead after 62 minutes when a long throw caused mayhem and Prutton turned superbly before slamming home from 10 yards.
Victory was secured in controversial style eight minutes from time, with Wednesday given a penalty for Simpson's tame challenge on Sanchez Watt. Lowe coolly sent Cisak the wrong way from the spot and Oldham could find nothing in response.