Brentford had goalkeeper Simon Moore to thank for their victory over Carlisle after his penalty save from Joe Garner.
The Bees led after 20 minutes when Jonathan Douglas volleyed home Harry Forrester's corner but six minutes later Garner took advantage of Harlee Dean's slip to level.
Paul Hayes scored the winner with a mis-hit shot after reacting quickly.
United had a chance to level when Tony Craig was ruled to have fouled David Symington but Moore was the Bees' hero.
VIEW FROM THE DRESSING ROOM
Brentford boss Uwe Rosler told BBC London 94.9:
"I was very pleased with the direction of the players in the second half.
"I wasn't sure after we played so poorly in the first half how it would affect us. The players responded very well and totally changed the character of the game.
"They did exactly what I asked them to do."