An Ezri Konsa own goal, a sublime Oliver Norwood strike and a Leon Clarke second-half winner were enough to consign the Bees to their sixth defeat in seven games.
Goals from Neal Maupay and Romaine Sawyers’ second-half deflected strike were not enough to ease the pressure on head coach Thomas Frank.
Maupay gave the hosts the dream start after just six minutes when he drilled home under goalkeeper Dean Henderson after a clever one-two on the edge of the box with Sawyers.
But the lead lasted just four minutes, when a completely unchallenged Konsa bizarrely glanced a header into his own net.
United stretched their lead five minutes later, Kieron Freeman teeing up Norwood to curl a beauty around and over Daniel Bentley and into the top corner.
The Blades should have made it thBees defence and only a brilliant point-blank stop from Bentley denied David McGoldrick.
Norwood’s free kick just before the break was stopped beneath the angle by Bentley and Canos flashed a volley over the bar at the other end.
Brentford emerged brighter after the break, Yoann Barbet fizzing a low drive just past the upright and Maupay’s shout for a penalty after being bundled over by Jack O’Connell in the box was waved away by Stephen Martin.
But the hosts levelled in the 65th minute when Sawyers fired a rasping drive past Henderson with the help of a John Fleck deflection.
Second-half substitute Clarke almost gave the visitors the lead straight from the kick-off but powered his header wide.
But he made amends minutes later when he sidefooted home Conor Washington’s low cross.
Maupay fired an instinctive effort just wide and Alan Judge’s free kick was parried by Henderson in the closing seconds.
Brentford: Bentley, Dalsgaard, Konsa, Mepham, Barbet, McEachran (Da Silva 77), Sawyers, Judge, Macleod (Odubajo 77), Canos (Marcondes 53), Maupay. Unused substitutes: Henry, Clarke, Daniels, Oksanen.
Sheffield United: Henderson, Basham, Egan, O’Connell, Freeman, Lundstram (Coutts 67), Norwood, Fleck, Stevens, McGoldrick (Clarke 60), Washington (Sharp 77). Unused substitutes: Stearman, Johnson, Moore, Duffy.
Referee: Stephen Martin (Staffordshire).