The scoring was started in the 63rd minute when defender Oliver Arblaster deflected an attempted cross past Ivo Grbic and into the bottom right corner of his own net.
Brentford thought they had put the game to bed just six minutes later when Mikkel Damsgaard volleyed home from just outside of the area, but the goal was cancelled following a VAR check that determined Oliver McBurnie was fouled in the process.
Sheffield United stayed in the game but were unable to create many chances, and with their focus set on attack, the hosts caught them lacking concentration from a throw-in as they scored a second in the 93rd minute.
Frank Onyeka, who had only been substituted on three minutes earlier, was found with a brilliant flick by fellow substitute Kevin Schade before hammering the ball into the net with just his second touch.
The result sees Brentford finally bring an end to a lengthy spell of nine games without victory, pulling them up the table and creating a much healthier gap of seven points between themselves and the relegation zone.
As for the visitors, this defeat comes as a crushing blow to their efforts to stay in the division as they remain rock-bottom of the Premier League table, four points behind 19th-placed Burnley who secured a draw in their match against Brighton.
With just six games remaining until the end of the season, and the Blades set to face three of the top seven in this time, Chris Wilder's side have an extremely tough task ahead of them if they are to miraculously remain in the division.
Ben Brereton Diaz was Sheffield United's largest threat, with the Chilean squandering a fantastic chance in the opening 10 minutes when the forward was charging in on goal, only to fail to make any real contact with his shot as Mark Flekken was able to comfortably collect it.
The chances were limited for the remainder of the first half, with the next biggest opportunity seeing Mathias Jorgensen's effort ruled out by the linesman for an offside in the 55th minute.
Brentford continued to harass the Blades' backline throughout the second half, with a seeming target to find Yoane Wissa and Bryan Mbuemo in behind the defensive line.
While neither of the wingers were able to get on the scoresheet, Thomas Frank will be more than happy with a vital three points that puts them in a great position to secure their spot in the top flight for another season.