Goals from Lasse Vibe and Florian Jozefzoon earned the hosts a 2-0 win. Danish striker Vibe gave the Bees the lead after 20 minutes with his sixth goal in five games when he finished off a flowing four-man move down the right.
He raced on to a Nico Yennaris through-ball to fire past Wednesday keeper Joe Wildsmith.
And Jozefzoon made sure of the points with a cool strike seven minutes from time, picking his spot from 12 yards after Neal Maupay won the ball on halfway and unselfishly played him in.
Brentford’s victory was just reward for some impressive one-touch football and only Wednesday keeper Joe Wildsmith kept the scoreline down.
The young keeper pulled off a string of last ditch saves to restrict the Bees to just the one goal at the break.
Wednesday threatened after 12 minutes when Atdhe Nuhiu headed Morgan Fox’s left-wing cross just wide, but from then on the first half was all Brentford.
Five minutes after taking the lead through Vibe, Romaine Sawyers carved open the Wednesday defence with a superb disguised through-ball, but Jozefzoon’s first-time angled drive was well saved by Wildsmith.
The keeper was called into action again less than 10 minutes later, this time diving full stretch to brilliantly save a Ryan Woods effort from 12 yards.
Moments later he then raced off his line to get a decisive touch to Vibe’s instinctive first-time shot after the visitors’ defence was again left flat-footed by a Sergi Canos pass.
Sam Hutchinson appeared lucky to escape with a yellow card almost on the stroke of half-time following an off-the-ball incident that floored Jozefzoon and incensed the Bees players.
Brentford kept their foot on the gas after the break, Jozefzoon ghosting past four challenges from the right to tee up Vibe, whose shot was deflected inches over.
Yoann Barbet went close from the ensuing corner, but his volley from the tightest of angles back across goal drifted just wide.
Canos almost extended the lead on the hour mark, but his speculative volley from the edge of the area fizzed just over.
Wednesday rallied late on and Adam Reach saw a rare effort blocked by Barbet before Lucas Joao should have done better when he glanced Jacob Butterfield’s left-wing cross agonisingly over.
But Jozefzoon’s late strike gave Brentford the scoreline their dominance deserved.
Wednesday caretaker boss Lee Bullen praised his side’s resilience and work rate, but said they were hit by a “sucker punch” as they chased the game.
He said: “The boys’ effort was outstanding and I think the fans could see that, but that’s the minimum you require and they have given us that today.
“The best team won the game but at 1-0 down you think we will have a go for it and just as we were adjusting, we got done by a sucker punch.”
He added: “Brentford are so tidy on the ball, so the best bit about half-time was getting in at only one down.
“We were a little bit more controlled in the second half and hoped for a break or shot or header, but it never materialised and you have to give Brentford credit for that.”
Bullen was disappointed his team could not carry the form from the 3-0 win at Nottingham Forest into the game at Griffin Park, but insisted he was now looking forward to the visit of Burton.
He said: “We came into the Brentford game with confidence but we could not give get the same movement we did against Forest, but the best thing is that we have the opportunity to right the wrongs of the previous game and it will be another hard-fought battle with Burton because you know what you get from Nigel Clough’s teams.”
Brentford: Bentley, Yennaris, Mepham, Bjelland, Barbet, Woods, McEachran (Mokotjo 69), Jozefzoon, Sawyers, Canos (Watkins 70), Vibe (Maupay 80). Subs Not Used: Macleod, Judge, Clarke, Daniels.
Sheffield Wednesday: Wildsmith, Palmer (Hunt 68), Loovens, Pudil, Fox, Hutchinson, Butterfield, Wallace (Abdi 46), Reach, Rhodes, Nuhiu (Lucas Joao 46). Subs Not Used: Jones, Marco Matias, Dawson, Frederico
Referee: Tony Harrington (Cleveland).