BEES boss Martin Allen admitted his side nearly became a shock cup casualty at League Two basement club Stockport.
Allen's League One highfliers reached the fourth round for the second successive season.
But the London club trailed 2-1 and had to rely on Isaiah Rankin's late strike to progress.
"Stockport sensed blood and they probably thought they had us," confessed Allen.
"They were a tough test for us but we could have won the match in the first half if poor finishing hadn't let us down."
Lloyd Owusu drove Brentford ahead from 20 yards but within four minutes Jermaine Easter raced clear to equalise having been put through by Damian Allen.
Keith Briggs then headed the hosts in front from Matt Hamshaw's corner.
Dudley Campbell levelled when his header looked to be cleared off the line by Allen but the assistant referee ruled the ball had crossed the line.
But Rankin's six-yard effort won it for the Bees.
Stockport caretaker boss Jim Gannon said: "It was one hell of a cup game.
"It's pleasing to see we can bounce back from behind and I was proud of the lads' effort."