Story of the match
It was the hosts who had the first chance of the game, Saman Ghoddos was forced into taking a pot shot from range, which was blocked twice by the Millers defence, before Mads Roerslev won a corner which was cleared.
Ghoddos then fired a dipping cross-come-shot from the right, it bounced in front of Blackman who claimed it on the second time of asking.
The first chance for the Millers came on 14 minutes when Michael Smith headed just wide from a Wes Harding cross from the right.
The visitors then had a chance when Jamie Lindsay saw an curling effort from the edge of the area saved by David Raya.
Rotherham went close again as Charlie Goode was penalised for handball, Ryan Giles delivered a decent free-kick from the left, it found Richard Wood who got free from his marker but his header went just wide of the right-hand post.
They went close again soon after, Wood knocked the ball down brilliantly for Angus MacDonald, the defender fired a volley over the bar.
Despite a good little spell by the visitors, it was them who fell behind, Canos clipped a lovely cross in towards Mbeumo to head beyond Blackman.
There was almost an instant response from Paul Warne's side, Smith produced a good cross which found Chiedozie Ogbene, whose header was saved by Raya.
Canos then dragged an effort into the side netting of the left-hand upright, before Toney fired an effort off the post after a neat flick from Emiliano Marcondes, despite pressure from MacDonald.
The first chance of the second half fell to the hosts, Toney who managed to get free from the visitors’ defenders, saw his header saved by Blackman.
Marcondes fired an effort across the face of goal from just inside the penalty area but the effort went wide.
Brentford then appealed for a penalty as Mbeumo went down under a shoulder charge by Giles but the referee waved away the appeals.
Brentford continue to look for a second, youngster Mads Bidstrup, collected a pass from Tariqe Fosu, before firing over the bar.
Rotherham tried to get an equaliser when substitute Kieran Sadlier fired an effort from 20 yards, however, it took a deflection and looped into the arms of Raya.
Millers hopes of staying-up out of their hands
Rotherham United's hopes of staying in the Championship for another season is now out of their own hands as the Millers fall to yet another defeat this campaign and back-to-back 1-0 defeats.
The Millers didn't really create anything from the game and it looks as their survival hopes are now running out.
Brentford: Raya, Goode, Pinnock, Sorensen, Roerslev, Ghoddos (Forss 74), Janelt (Jensen 89), Marcondes, Canos (Fosu 74), Toney, Mbuemo (Bidstrup 74).
Subs (not used): Daniels, Norgaard, Reid, Stevens, Gordon.
Rotherham United: Blackman, Harding (Olosunde 77), Ihiekwe, Wood (Ladapo 66), A MacDonald, Giles, Lindsay (Barlaser 77), Wing, Wiles (Sadlier 85), Ogbene (Hirst 77), Smith.
Subs (not used): Vickers, Clarke, S MacDonald, Jozefzoon.
Referee: Michael Sailsbury
Assistants: Mark Pottage and Robert Merchant
Fourth Official: Andy Davies