Wahorn and James McClean continued to create a number of chances as the home side started to dominate, but the Owls were able to fight their way back into the game shortly before the break.
As Wednesday started to look the more likely of the two sides to force a lead before the break, Ali Al-Habsi rushed off his line to deny Jacques Maghoma, but gave away a penalty as he brought the winger down.
Leon Best stepped up to take the spot kick, but the Wigan keeper made amends, punching the strike away from the goal to keep the team level at the break.
The visitors continued to have the better of the chances early in the second half, forcing the hosts into a double substitution less than 10 minutes after the restart.
Callum McManaman immediately looked to test the Wednesday defence, but gave away a foul while battling with the right-back.
Gomez managed to pick out James Perch with a well-timed cross into the box, but the visitors cleared his header off the line.
Wigan continued to get stronger as full time approached, as McManaman set up Marc-Antoine Fortune for a volley which sailed just wide while another cross was cleared shortly after.
Their persistence paid off as they were awarded a penalty inside the final three minutes when Caolan Lavery brought down Perch, which Gomez swiftly converted to give Wigan all three points.