Goals from Yoane Wissa, Bryan Mbeumo and Saman Ghoddos secured a first home win of the season for Brentford.
The Bees, who had not tasted victory since beating Fulham in the second game of the season, dominated from the opening whistle in what was an impressive display against the newly-promoted Clarets, who have now lost seven of their first nine games and remain in the bottom three.
Thomas Frank’s side took a deserved 25th-minute lead when Wissa turned in Mbeumo’s cross after Neal Maupay dispossessed Sander Berge and played in the Cameroon international.
Brentford should have been well in front at half-time, with Maupay having a header disallowed after Kristoffer Ajer was adjudged to be narrowly offside in the build-up by VAR.
The on-loan Everton forward then missed a golden opportunity to score his first goal in more than a year when he was put clean through by Frank Onyeka but could only shoot straight at James Trafford, who then made fine saves to deny Mbeumo and Wissa.
The second half continued in a similar fashion with Brentford well on top and they doubled their lead with a superb curling finish from Mbeumo after he was teed up by Maupay.
Burnley should have pulled a goal back when Zeki Amdouni was found by a low cross from Lyle Foster but he somehow miscued wide with the goal at his mercy.
The visitors were then reduced to 10 men when Connor Roberts was sent off for a second bookable offence after hauling down Wissa, before substitute Ghoddos added some extra gloss to the scoreline with his first touch when he fired home from 25 yards three minutes from time.
Brentford: Flekken, Ajer, Pinnock, Collins, Onyeka (Ghoddos 84), Jensen (Yarmolyuk 75), Norgaard, Janelt, Mbeumu (Olakigbe 88), Maupay, Wissa.
Subs not used: Strakosha, Zanka,, Mee, Roerslev, Kim, Brierley.