Yoane Wissa got the ball rolling in the first half, before two second-half wonder goals from Bryan Mbeumo and Saman Ghoddos clinched the points for Thomas Frank's men, who remain 15th despite the win.
The hosts were dominant for large periods, and Burnley keeper James Trafford was kept busy, especially in the first half.
Defeat for Vincent Kompany's side keeps them in the bottom three, as the Clarets remain in 18th after nine matches.
Brentford were quickly out of the traps, and thought they took the lead when Neal Maupay fired home from the second phase of an Mbeumo free-kick.
However, the assistant's flag went up and on VAR review, the decision stood with two Brentford standing in offside positions when the free-kick was taken, meaning Maupay is still waiting to end his 34-game scoreless streak.
Burnley hardly threatened in the opening 45 minutes, and goalkeeper Trafford was responsible for keeping the score down, even if he was fortunate to get away with overplaying after Wissa blocked his pass out, only to see the ball flash narrowly wide.
Just moments later though, Trafford was picking the ball out of his net, when Mbeumo's perfectly weighted square ball found Wissa at the back post who had the simplest of finishes to convert from close range.
Brentford smelt blood and continued on the front foot, as Maupay was gifted an opportunity after Ameen Al-Dakhil conceded possession, but his tame effort was kept out by a combination of Trafford and the backtracking Dara O'Shea.
After conceding possession again too easily, Kompany's men were caught on the counter and Mbeumo's powerful effort was turned away well by Trafford.
The visiting goalkeeper would go on to make more important stops towards the end of the first half, keeping both Maupay and Christian Norgaard, via a Wissa deflection, at bay.
Zeki Amdouni had Burnley's only real opening of the first half when he fired on goal when unmarked, but his effort was well saved by Mark Flekken.
Frank may have been a little disappointed to only go in at half-time 1-0 up, as his side had 15 efforts on goal in the first 45, seven of which were on target.
Burnley looked revitalised after the restart too, especially after the introduction of Luca Koleosho, and within seconds of coming on he forced a foul out of Kristoffer Ajer, who was booked as a result.
Koleosho sprung the game into life, and it was his long-range effort which was blocked out for a corner that had the Burnley fans on their feet.
However, despite that positive start to the half, Burnley were undone by a piece of class when Mbeumo added Brentford's second just after the hour mark.
Maupay's nice layoff for the Cameroonian forward allowed him to unleash an unstoppable strike right into Trafford's top corner, leaving the goalkeeper with no chance.
The hosts could have been accused of a bit of complacency at 2-0 up though, as Lyle Foster found himself with lots of space on the left-hand side, and his ball into the area found Koleosho, but with the goal gaping, the Italian inexplicably missed his kick completely and failed to hit the target.
After wasting another promising opening just moments later, the game got away from Burnley when Connor Roberts was sent off for a second bookable offence after a tug on Wissa.
Burnley were unable to retain possession from that point, and the final nail in the coffin came from sub Ghoddos, who scored just his second Premier League goal with a phenomenal strike from the edge of the box which gave Trafford no hope once again.
Brentford continued to put the pressure on in seven minutes of added time, and despite more Burnley overplaying presenting them with opportunities, the Bees were unable to add to their tally.
The win ends a six-game winless streak for Brentford, with another 3-0 success over Fulham on the second weekend of the season their only other victory so far this season.
Brentford now travel to West London rivals Chelsea in the Premier League's Saturday lunchtime fixture next weekend.
After a seventh Premier League defeat of the season, Burnley face relegation rivals Bournemouth at the Vitality Stadium next.