There had been nothing in the game for 43 minutes, before Wallace's close-range effort took a wicked touch off defender Jake Buxton to deceive goalkeeper Jakob Haugaard.
Wigan edged a similarly tight second period, but did not really do enough in the final third to test Keiren Westwood in the Wednesday goal.
Their best chance came at the three-quarter mark, but new boy James Weir - on loan from Hull City - could not hit the target with a free header from 12 yards.
The result sees Wigan remain third-bottom of the Championship, ahead of this weekend's programme.
