The Owls capitalised on Callum McManaman's reckless red card mid-way through the second half as giant striker Atdhe Nuhiu headed the winner shortly after.
Manager Stuart Gray was pleased with the three points, he said: “Obviously, I’m pleased with the win and that is first and foremost.
“The only thing I would say was disappointing was the fact that we got the one goal but didn’t put the game to bed.
“Every team in this division has players who can hurt you and Wigan nearly did that right at the last. That is a part of our game we must improve, but for now, we will enjoy the win.
“I’ve said it before that this division is wide open. Possibly even more so than the last couple of seasons.
“Not a lot of teams are showing any real consistency and the places are there for someone who can. That’s back to back wins for us now and I’ve said to the players, always look up, never look down.”
The result leaves Wednesday up in tenth place, six points of a play off place.