They stretched their lead on the half hour as Dasilva teased his marker before slipping a slide-rule pass to top scorer Watkins, who turned and fired low past the keeper from close range.
It was four shortly afterwards when patient build-up play was rewarded as Jensen passed the ball home with a clever reverse finish inside the near upright.
Dasilva grabbed his first of the afternoon five minutes before the break when he toyed with two Hatters defenders before moving the ball onto his left foot and curling a beauty just inside the far post from the edge of the box.
He added to his tally in first-half stoppage time, firing home a low drive with his less-favoured right foot after a slick eight-man move.
Luton’s cause was not helped when half-time substitute Brendan Galloway went down off the ball moments after the restart and was stretchered off leaving Luton to play out the game with 10 men.
Brentford were ruthless, and despite being in the comfort zone they added two more to their tally, leaving them two short of the club-record 9-0 win over Wrexham in 1963.
First Pelly Ruddock inexplicably hauled down Watkins in the box with the ball going out of play and Benrahma coolly sent Shea the wrong way from the spot in the 70th minute.
And the mauling was complete four minutes from time when the Bees carved open the visitors’ defence once more and Potts felled Benrahma for Dasilva to secure his hat-trick.
It could have been double figures for the Bees in a one-sided affair that saw Bees goalkeeper David Raya only forced into action once when Ruddock forced a smart save low down to his left early on.
Watkins was denied by the legs of Shea midway through the first half after a lightning quick interchange between Dasilva and Benrahma, before centre back Ethan Pinnock saw a far-post header cleared off the line by James Bree.
The Hatters survived what looked like a clear penalty shout when Mbeumo was hauled back in the box, but it was only a temporary reprieve.
After the interval Dasilva and Mbeumo both went close with long-range dipping efforts before Benrahma forced a save from Shea with a cheeky free-kick that almost beat him at the near post.
In the end the whistle could not come soon enough for Luton, who have not shipped seven since a 7-1 FA Cup defeat at Grimsby in 1996 and were only one off the 8-1 defeat suffered at Lincoln in December 1966.