With both teams playing with high defensive lines at Hillsborough there were a high number of long balls attempted by each side but, with few finding their mark, the game produced nothing of note for the vast majority of the first half.
It took until the 35th minute for a decent chance to present itself when a whipped cross found Caolan Lavery in the box but the Owls striker could not wrap his foot around it and the ball sailed wide of the post.
The second half started in a livelier fashion to the first and that was evident after 49 minutes when some clever play from Brentford around the box presented Andre Gray with an opportunity to get a shot on goal but his effort skimmed agonisingly past the post.
However, the promise of exciting football and the chance of goals petered out as the half wore on. Both sides managed to work themselves into good areas but could not produce the final pass to create clear-cut scoring opportunities.
A mistake from Harlee Dean looked as though it had gifted Wednesday with a sure-fire goal. Sergiu Bus collected the ball and made a run towards goal with Chris Maguire at his side but the pair could not make the two-on-one situation count as Bus’ lay-off to Maguire was hit straight into the midriff of James Tarkowski.
The breakthrough finally came in the 75th minute when Lee ghosted into space in the box and was unmarked as a parried ball from David Button fell at his feet. He made sure his shot found the back of the net as he rifled home from six yards out.
Brentford had a chance to strike back five minutes later but, having found himself one-on-one with the goalkeeper and with two of his team-mates to the left of him, Alan Judge blasted the ball over the keeper and over the goal.
Another mistake from Dean almost gifted the Owls a second goal but instead of running into the space he had available, Bus decided to shoot from outside the box and could not keep his effort on target.