First-half goals by Chris Wood, Matthew Lowton and Maxwel Cornet staked the Clarets to a 3-0 lead inside 36 minutes. Saman Ghoddos grabbed a late consolation for the Bees, who have lost three matches on the trot.
The match also marked the nine-year anniversary of Sean Dyche taking charge of Burnley and his side rewarded him with their best effort of the season.
Story of the match
The opening goal of the game came after just four minutes. A ball from back to front by Lowton skipped off the turf and Ethan Pinnock was unable to make an interception as he stretched out his left leg.
A touch The ball found Wood and he smashed a first-time shot across Alvaro Fernandez and into the far corner. He had two further chances ruled out for offsides and a foul, respectively.
On 15 minutes, Burnley thought it was two as Johan Gudmundsson found Wood down the right and he nodded on to Cornet, who poked home from close range, but Wood was offsides when the ball was played, so the goal was ruled out.
Pope was then saved by his defence after he spilt a long throw, but the shot from Canos was headed over the bar by skipper Ben Mee.
Ashley Westwood then released Gudmundsson, but Fernandez denied him. James Tarkowski then headed the ensuing corner over.
Burnley did find a second when Charlie Taylor measured a cross and Lowton got in between two Brentford defenders to get under the ball and head it in from eight yards out.
Four minutes later, the hosts put the game to bed. Dwight McNeil played a ball in behind for Cornet, who took a touch, cut back and blasted a shot past Fernández and into the top corner from 18 yards.
A Cornet pass released Guðmundsson as he strode into the penalty area. Henry got back to make a recovery tackle but Pontus Jansson and Christian Norgaard got in a tangle as they attempted to clear and a shot from Wood deflected wide.
Early in the second half, Pope pushed away a Norgaard chance from 18 yards out on the full stretch and at the other end, Wood headed wide as the game continued to be end-to-end.
The Bees nearly got on the board as Toney had a shot blocked, but he managed to toe-poke the ball past Pope, Lowton there to prevent Marcus Forss from converting.
Chances were coming for the visitors, Forss seeing his blocked inside the six-yard box. Nørgaard then curled an effort wide and Toney let fly from 20 yards, but his shot went over the bar.
After McNeil curled a free-kick wide from an ambitious angle, Brentford pulled a goal back. Vitaly Janelt had time to measure a pass in to the penalty area, to find Nørgaard at the back post and Ghoddos volleyed past Pope.
Ghoddos then hit the wall with a free-kick and the follow-up from Janelt flew straight at Pope through a crowd of bodies. Forss then had a shot blocked as Brentford pressed without success.
Man of the match: Chris Wood
He opened the scoring and was lively throughout, having several chances to add to his tally. With the emergence of Cornet to compliment him in attack, the New Zealander should have even more opportunities in the matches to come.