The Scotland international scored either side of half-time after Chris McCann opened the scoring in the Sky Bet Championship clash at Hillsborough.
Owls striker Atdhe Nuhiu headed over in the opening stages before Wigan winger Callum McManaman cut inside from the right at the other end and tested goalkeeper Keiren Westwood at the near post.
The home side almost edged ahead with 18 minutes played when midfielder Jose Semedo, who has registered just one Wednesday goal in four seasons with the club, struck the left-hand upright with a low strike from the edge of the box.
Wigan midfielder McCann then went one better, opening the scoring in the 26th minute.
James McClean curled an inswinging corner into the box from the right and McCann sent a powerful header into the roof of Westwood’s goal.
Wednesday did not have to wait long to respond and equalised a minute later with their first goal in four games.
On-loan midfielder Lewis McGugan’s ball into the box was recovered by Austrian Nuhiu and he teed up unmarked strike partner May for a simple close-range finish past Latics goalkeeper Scott Carson.
The quick reply lifted the home crowd and minutes later Dutch winger Royston Drenthe slipped through Jeremy Helan on the left but the full-back was denied by an outstretched arm from Carson.
McManaman’s 20-yard shot was saved by Westwood 10 minutes prior to the the break before the Owls keeper turned Marc-Antoine Fortune’s low shot behind for a corner.
The visitors almost regained the lead eight minutes after the restart when a scrambled goal-bound header was cleared off the line by McGugan following a Ben Watson corner.
Goalscorer McCann then diverted McManaman’s low cross wide of the Wednesday goal before May turned the contest in the Owls’ favour in the 71st minute.
The summer signing from St Johnstone met Chris Maguire’s cross from the left and his header hit both posts before being adjudged to have crossed the line.
Adam Forshaw narrowly failed to connect with McManaman’s right-wing centre with 17 minutes remaining before the latter flashed an effort across goal as Malkay Mackay’s men pushed for a leveller.
Wigan went close again in the 86th minute when McClean outpaced the Wednesday backline before rolling an effort towards goal which was cleared by Liam Palmer.
The away side were given four minutes of injury time in which to find an equaliser but Wednesday held firm to claim a second home success of the season.