Manager Sean Dyche celebrated his ninth anniversary of taking charge of the East Lancashire club in the best way possible as the Clarets delivered their most convincing display of what has been a testing campaign.
Chris Wood fired Burnley ahead in the fourth minute with a superb first-time strike after Ethan Pinnock had failed to deal with a long pass forward from Matt Lowton.
Maxwel Cornet thought he had made it 2-0 but a VAR review ruled the effort out for offside but the second goal came soon enough with Lowton getting in between two defenders to head a Charlie Taylor cross past the stranded Alvaro Fernandez.
Ivorian Cornet, however, made sure there was no debate about his next effort.
Collecting the ball from Dwight McNeil he made space for himself before unleashing a superb shot into the top corner to make it four goals in five appearances since his move from Olympic Lyonnais.
Brentford pulled a goal back in the 79th minute through a brilliant volley from substitute Saman Ghoddos and enjoyed late pressure but Burnley held firm to break their winless streak.
"We haven’t been far away. We really took the game on in the first half. The performance was good but there were some great finishes as well," said Dyche.
"There was a real determination in the group. Maxwel Cornet has hit the ground running for us. He’s still got things to learn in a positional sense in the Premier League," he added.
Burnley are 17th place in the table on seven points, above Leeds United on goal difference although Marcelo Bielsa's side play at bottom side Norwich City on Sunday. (Reuters)

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