In a match that was heading for a statement in blustery conditions, it was Gow - the most positive player on the field - who had the wherewithal to contrive the winning goal.
He took a short pass from Liam Craig to beat Roddy McKenzie with an angled shot which the goalkeeper managed to get a hand to but could not keep out.
It was cruel luck on Dunfermline and they must feel that even Mother Nature is conspiring against them.
The wind turned the game into a farce. Dunfermline started with the wind at their backs and had a couple of early chances.
Greg Shields steered a header wide of target from an Owen Morrison free-kick, before Jim O'Brien sent a left-foot shot wide from 16 yards when he should have tested debutant goalkeeper Kasper Schmeichel.
Falkirk improved as the half went on and were unlucky not to go in front when Dunfermline failed to deal with a Russell Latapy free-kick and Kenny Milne's netbound shot struck Gow.
Stevie Crawford had the only clear-cut chance of the first half, deep into injury-time when he pounced on an O'Brien head-flick, but Schmeichel closed the angles down quickly and blocked the striker's shot.
Patrick Cregg and Latapy worked an opening between them with a neat exchange of passes, but Latapy's final shot was timid and McKenzie saved easily.
Craig had a decent chance shortly afterwards when he cut in from the left but curled his shot high and wide.
His next contribution was more telling as he played Gow through and, with a suspicion of offside, he did not hesitate and squeezed the ball home.