Three superb first-half goals condemned Brentford to a third straight Championship defeat and a second in a row at home.
Scott Arfield, Joey Barton and George Boyd all found the net from the edge of the box before the 40th minute.
Brentford rallied in the second half but an 11th goal of the season for Alan Judge, one of two Brentford players Burnley are trying to sign, proved a mere consolation.
The Bees looked deflated from the outset after first-choice centre-back James Tarkowski – the subject of a failed £2.5m bid from the Clarets last week – refused to play before kick-off.
Burnley also have an offer on the table for Judge, while they started with former Bees striker Andre Gray up front, and they did not wait around to rain shots on the Brentford goal.
Gray, Arfield, David Jones and Stephen Ward all threatened before Arfield found the top corner to convert the away side’s dominance into an opener on 12 minutes.
In contrast, John Swift and Judge had meagre efforts on goal before former QPR midfielder Barton curled home a superb free-kick that went in via the post.
Arfield shot narrowly over just moments later and Gray should have converted one of two excellent chances inside the box, but Boyd added the third with a sweet volley on 39 minutes.
Brentford pushed hard to get back in the game, with Sam Saunders and Lasse Vibe introduced from the bench, while Judge noticeably improved and found the net from a tight angle 12 minutes into the second-half.
Both Judge and right-back Maxime Colin found the side-netting with further efforts but Burnley almost added a fourth late on when substitute Rouwen Hennings smashed a shot wide of the far post.
Brentford (4-3-3): Button; Colin, Dean, O’Connell, Bidwell; Diagouraga, Woods; Canos (Saunders 46), Judge, Swift (Yennaris 67); Djuricin (Vibe 46)
Subs not used: Bonham, Barbet, McEachran, Hofmann.
This post was last modified on 16/01/2016