Kieran Lee fired in to secure only a fifth home win of the season for the Owls who downed play-off chasing Brentford.
Lee popped up 15 minutes from time to secure a narrow win for Wednesday and deliver a hammerblow to the top six hopes of the visitors.
Brentford arguably carried the greater threat throughout the night but failed to trouble Keiren Westwood.
And the Owls performed admirably, particularly Filipe Melo on his full home debut.
Stevie May drew a save from David Button as Wednesday made a strong start.
The Owls striker resisted the temptation to go down under pressure and fired on goal, drawing a decent stop from the Bees keeper.
Brentford fired the first real warning shot as they looked to push back into the top six with victory.
Jonathan Douglas played in Andre Gray who held off Tom Lees only for his shot to deflect wide for a corner.
Button was alert to prevent Wednesday from taking the lead during their bright start to the game. With Lee lurking, he rushed out to claim Caolan Lavery’s cross with the Owls midfielder sliding in.
Gray was a threat for Brentford and fired wide after bursting past Tom Lees midway through the half.
Lavery failed to find the target for Wednesday after meeting a cross from Lewis Buxton.
Melo, on his first start at Hillsborough, had Button scrambling across goal to try and keep out a speculative effort but it flew wide.
Judge rattled the crossbar as Brentford threatened late in the first half.
Gray produced a sublime backheel which Judge ran on to and carried the ball clear into the box but blasted back off the woodwork.
Gray went close to giving Brentford the lead early in the second half.
The Bees forward fired just wide with his first effort of the second period.
But it was Wednesday who broke the deadlock on 75 minutes.
The Owls broke in numbers and Lee was well placed to sweep home after a fine touch from substitute Sergiu Bus.
Judge missed a glorious chance to level up after being put clear through on goal, blasting over the bar from 12 yards out with eight minutes remaining.
Bus could have wrapped things up for the Owls in stoppage time but fired over the bar after darting through.
Wednesday: Westwood, Buxton, Lees, Zayatte, Helan, Lee, Melo, McGugan (Maghoma 74), Isgrove (Maguire 59), May (Bus 59), Lavery.
Subs not used: Kirkland, Kelhar, Vermijl, Nuhiu.
Brentford: Button, Bidwell (Smith 81), Dean, Douglas, Odubajo, Dallas (Toral 65), Judge, Gray, Diagouraga (McCormack 81), Jota, Tarkowski
Subs not used: Craig, Bonham, O’Connell, Udumanga
Referee: Mark Brown (East Yorkshire)