Mbeumo opened the scoring in scrappy fashion in the first half before setting up Saman Gheddos for the second, with Mads Bech Sørensen heading home the third late on.
The Owls remain two points from safety after suffering their fourth defeat in five games.
Story of the match
The first half that ensued was a very scrappy and uneventful 45 minutes, with neither side being able to stamp their authority on the fixture.
The Owls had the game’s opening effort, as Kadeem Harris took a wayward pass from Vitaly Janelt into his stride before playing the ball into the feet of Barry Bannan, who strayed inwards from the left and forced David Raya into action, pushing the effort past his near post.
The following corner saw Tom Lees head wide at the back post from Bannan’s delivery.
On eight minutes, Brentford had their first sight on goal after Mathias Jensen dispossessed Elias Kachunga on halfway. The tackle rolled into the feet of Ghoddos, who picked out the back-post run of Mbeumo, but the forward volleyed over.
The Owls certainly looked the side who attacked with more intent in the opening exchanges, however, it was the Bees who would take the lead in the 24th minute.
A long throw into the area caused a scramble, with the ball remaining uncleared before Mbeumo headed home Sergi Canós’ miscue to net his fourth goal of the campaign.
Wednesday quickly pressed for an equaliser to try and avoid a 12th straight defeat when going behind first, and responded well to the opener, sending numerous crosses into the area, but to no avail.
The Wednesday squad went into the break with their heads down, as they looked like a side massively deprived of confidence.
Brentford almost doubled their lead on 53 minutes, as Gheddos took advantage of lackadaisical defending from the visitors, finding time and space before placing a low drive wide of the far post.
10 minutes after the restart, Liam Palmer drove forward from the Owls’ back three, however, his long-distanced effort flew well wide of Raya’s goal.
The Bees netted their second goal of the evening, with just over a quarter left to play. Toney’s neat touch took the ball into the path of Mbeumo, who subsequently teed up Ghoddos to drill home his third goal of the season.
Moments later, Mbeumo almost bagged his brace as he found himself clean through on goal, but his effort was well saved by Joe Wildsmith, who deputised for the injured Keiren Westwood.
Sørensen made sure that the three points were staying in London, heading home from Ghoddas’ set-piece to ensure that Thomas Frank’s side were back on the promotion trail.
It is vital that the Owls take maximum points from their next two fixtures, facing Luton Town at Kenilworth Road at the weekend before welcoming rivals Rotherham United to Hillsborough Stadium in a relegation six-pointer.