Griffiths, Wolves' 11-goal leading scorer, lashed a fierce 11th-minute drive against the foot of a post in an entertaining encounter.
It proved to be the closest either side came to scoring as the goals dried up for Brentford.
Uwe Rosler's team had scored 10 in their previous two league and cup games and had been chasing a seventh successive win.
But Adam Forshasw and Clayton Donaldson squandered excellent first-half chances, with Wolves goalkeeper Cark Ikeme also in impressive form.
Griffiths sparked the game into life when he hit a post after good work from Kevin Doyle - with Forshaw wasting a golden opportunity to give Brentford the lead just 60 seconds later when he blazed over the crossbar from just six yards.
Griffiths was in a lively mood and only a smart save from David Button denied him in the 20th minute before Donaldson narrowly failed to hit the target after he had outpaced the Wolves defence and chipped the ball over Ikeme.
Ikeme then frustrated Donaldson, with Griffiths out of luck again on the stroke of half-time, flashing a shot across the face of goal, before the Scotland international fired wide again in the 73rd minute.
Brentford made a late push to snatch the points but Toumani Diagouraga and Alan McCormack could not find a way past the assured Ikeme.