Ivan Toney scored twice in the final five minutes for Thomas Frank’s Bees to condemn the Clarets to a loss.
Toney headed in Christian Eriksen’s 85th minute cross prior to converting a penalty after he was fouled by Nathan Collins, who received a red card.
Sean Dyche made one change from last weekend’s game against Chelsea, with Maxwel Cornet returning to the starting line-up in place of Jay Rodriguez.
Captain Ben Mee remained out through a knee injury, so Collins continued at centre-back alongside James Tarkowski who took the armband against his former club.
First-half
The Clarets had an early opportunity in West London when Cornet was brought down by Vitaly Janelt for a free-kick. Josh Brownhill bent his right-footed effort narrowly wide of David Raya’s bottom left-post.
Forcing the issue, the presence of Wout Weghorst saw the Clarets earn several early corners, with the Burnley number nine putting Raya under pressure from a set-play, which the goalkeeper managed to deal with.
Burnley then had to do some defending as Sergi Canos’ blocked shot dropped for Bryan Mbeumo who hit the rebound over Nick Pope’s crossbar.
Pope then had to deny Eriksen’s fierce drive with a strong hand to turn the shot around the post.
The Clarets stopper had to be alert and quick off his line to beat Toney to the ball following Eriksen’s pass.
Cornet struck just wide of Raya’s goal after latching onto Dwight McNeil’s ball, with Dyche’s men pushing for the opener.
Beyond the half-hour, Ashley Westwood’s pinpoint cross found McNeil, but the winger could not direct his header on target.
In the closing stages of first-half play, Tarkowski was in the right place to clear Mbeumo’s drive across goal before Collins headed away Canos’ dangerous cross.
Second-half
Seven minutes after the break, Janelt got in-between Collins and Tarkowski, but he headed over Pope’s crossbar after Canos’ lofted cross.
Tarkowski was well-placed again minutes later to ensure Eriksen’s cross did not reach Toney.
Looking to make the breakthrough, Aaron Lennon’s cross towards the back post, aimed for Weghorst, was cleared by Rico Henry.
Dyche made his first change of the game on 68 minutes, replacing Weghorst for Rodriguez.
With 20 minutes left, Cornet battled past Ethan Pinnock to break through on goal, however Raya was equal to the strike.
Five minutes later, substitute Rodriguez almost put the Clarets ahead in emphatic style, as his drive from distance rattled the crossbar.
McNeil’s cross was steered behind by Pontus Jansson, while Brownhill’s ball was dealt with by the Brentford back-line.
But Burnley were behind on 84 minutes. Eriksen found space to deliver an inviting cross for Toney to power a header beyond Pope.
Collins was sent off by referee Paul Tierney for bringing down Toney after Eriksen’s pass in the box. The striker took responsibility to dispatch past Pope.
Burnley are next in action when they welcome Manchester City to Turf Moor on Saturday 2nd April.
Brentford: Raya, Henry, Pinnock, Jansson, Ajer, Janelt, Norgaard (Jensen 80), Canos (Wissa 74), Mbeumo (Onyeka 90), Eriksen, Toney
Subs not used: Lossl, Ghoddos, Jorgensen, Baptiste, Sorensen, Roerslev.
Burnley: Pope, Taylor, Tarkowski, Collins, Roberts, Brownhill, Westwood, McNeil, Lennon, Cornet, Weghorst (Rodriguez 68)
Subs not used: Hennessey, Lowton, Cork, Barnes, Stephens, Bardsley, Long, Thomas.
Goals: Toney, 84, 90+4
Sent off: Collins, 90+3
Referee: Paul Tierney