The Owls posted a welcome win at Hillsborough after three straight draws and put a dent in the play-off hopes of Brentford.
The recalled Kieran Lee scored the only goal of the game 15 minutes from the end to seal all three points – whilst equalling a club record 17 clean sheets in a league campaign.
The promotion contenders arguably had the edge in a contest of few openings, with Andre Gray twice going close.
Caloan Lavery almost struck for Wednesday and the Bees hit the bar through Alan Judge after Wednesday started well, with the recalled Kieran Lee playing a clever give and go with Lavery that ended with the midfielder being thwarted by Brentford keeper David Button.
But the visitors needed little time in finding their feet and Gray forced Keiren Westwood into action from a close range snapshot.
The game then slipped into an even affair with little goalmouth activity until Gray broke free down the right and advanced to stab beneath Westwood but just wide.
Wednesday hit back with Lavery narrowly missing the target from a Lewis Buxton feed before the Bees countered and Judge struck the crossbar two minutes shy of half time.
Brentford created more chances in the first half and started the second with zest as Gray motored along the edge of the box but planted his shot inches wide.
The Owls introduced Chris Maguire and Sergiu Bus from the bench on the hour but struggled to break down a resolute and well organised Bees defence – until they finally hit home on 75 minutes.
Lavery crossed low from the left, Bus swivelled to shoot and the ball fell invitingly to Lee, who drilled into the Kop net from eight yards.
Brentford had little choice but to chase the match and should have levelled on 80 minutes when Judge had time and space to pick his spot ten yards out only to blaze high and wide.
And equally, the Owls might have put things to bed at the last when Bus went through one on one but the Romanian also smashed over the crossbar.
Owls: Westwood, Buxton, May (Bus 59), Lavery, Lees, Helan, Zayatte, Lee, Isgrove (Maguire 59), Melo, McGugan (Maghoma 74)
Brentford: Button, Bidwell (Smith 81), Dean, Douglas, Odubajo, Dallas (Toral 66), Judge, Gray, Diagouraga (McCormack 81), Jota, Tarkowski