The Bees went in two-up at the break after a quality finish from Clayton Donaldson and goal of the season contender from Harry Forrester.
Donaldson struck after three minutes, deftly glancing home Toumani Diagouraga's left-wing cross at the near post and Forrester made it two on the half-hour, turning brilliantly on halfway before smashing home a grasscutter from fully 25 yards.
Brentford were in almost total command before the break, but had to withstand wave after wave of pressure from the Blades in the second period and Bees goalkeeper Simon Moore, who had tipped Shaun Miller's point-blank header over before the break, had to be at his best to deny Nick Blackman in a one-on-one on the hour-mark.
Brentford loan signing Marcello Trotta thought he had calmed the host's nerves late on, but his tap-in after a Harlee Dean piledriver was parried clear, was ruled out for offside.
Miller's goalbound effort was cleared off the goalline by Donaldson in the dying minutes as the visitors lost their composure, Harry Maguire escaping with a yellow for a lunge on the striker when it might have been red.