In what was a contentious decision, Gow was given his opportunity – which he duly converted – to put the Magpies ahead in the 26th minute when he went down under pressure from Mark Beevers.
After Njogu Demba-Nyren spurned an opportunity to double the advantage on the stroke of half-time, the visitors continued to dominate after the interval.
Demba-Nyren was denied by the foot of the Wednesday goalkeeper before Ivan Sproule fired wide after good approach play.
The Owls came back into the game after that, though, with Clinton Morrison seeing his goalbound header well saved.
And, despite creating a couple of openings late on, Wednesday fell to a defeat which leaves them looking over their shoulders in League One.