Midfielder Sam Hutchinson failed a fitness test before kick-off, but Keiren Westwood and Kieran Lee were fit despite picking up injuries last week at Birmingham City.
Atdhe Nuhiu started up front, with Aiden McGeady dropping to the bench.
The vistors twice threatened in the early exchanges, but were down to 10 men when Yoann Barbet pulled Gary Hooper back and the red card was shown.
Ross Wallace’s free-kick was saved, but the Owls were in front on 12 minutes.
Daniel Pudil’s cross was deflected and Fernando Forestieri headed home from eight yards out.
It was 2-0 on the half hour. Keiren Westwood’s booming kick downfield saw Hooper race behind the back line before volleying home.
And the Owls made it 3-0 just before half-time, Keiran Lee finishing off a flowing move after good work from Barry Bannan and Hooper.
The second half failed to bring any further goals until the 89th minute.
Substitute Lucas Joao broke clear on the right, and blasted home in front of the Kop to cap a professional display by the Owls.
Wednesday boss Carlos Carvalhal was not getting carried away with his team’s promotion prospects.
“We played well,” the Portuguese said. “We now have one week to prepare for Preston.
“I think that the red card was was clear, as (Hooper) was through on goal, one on one.
“Even though they were down to 10 men, we prepared very well, explored our spaces, moved the ball and changed the speed.
“More important to me was the transition, the way we worked when we lost the ball. We were organised enough not to give Brentford opportunities.”
Carvalhal continued: “My consideration is the same as the beginning. We are outsiders in this competition. We have a new coach, 15 or 16 new players.
“We are not the favourites. We don’t want to lose focus. The position (fifth) is not important if we don’t win the next game.
“For me, the most important thing is the team. Everything will be good if you win the next match. Everything around this, records, best player, best coach and so on, is artificial.
“Preston is the most important. We know it will be a tough game. We must be ready for a really really tough game.
“The position? Let’s see in May.”
Brentford manager Dean Smith felt his side were unlucky to go down to 10 men.
“The result is a consequence of something we have no control over,” he said.
“For me, I don’t believe the referee (Scott Duncan) can make the decision. I think he guessed. He’s directly behind it, 40 yards away. I thought it was a poor decision.
“I don’t think Gary Hooper has the ball under control. He’s gone down easily.
“They’ve got really good players going forward, but we always felt we had a game-plan. Unfortunately, this changed after six or seven minutes.
“I think they’ve got a really good shot at promotion with the players they’ve got.
“The future for us is the next game. We felt that that team could hurt Sheffield Wednesday but unfortunately that decision was taken out of our hands, whether it would have been a good game or not.”
Owls: Westwood, Hunt, Lees, Sasso, Pudil, Bannan, Lee, Wallace, Forestieri, Nuhiu, Hooper. Subs: Price, Turner, Semedo, McGugan, Bennett, Joao, McGeady.