The former Peterborough United striker guided a header from Christian Eriksen’s cross past Nick Pope with just five minutes remaining.
The 25-year-old, who previously bagged a hat-trick away at Norwich City, then scored from the spot with the last kick of the game after Nathan Collins received Burnley’s first red card in 120 games.
The visitors had been wasteful in front of goal with Maxwel Cornet failing to convert from inside the box in both halves, Dwight McNeil got his header all wrong when getting on the end of Ashley Westwood’s delivery, while substitute Jay Rodriguez’s howitzer came back off the crossbar.
The result keeps Sean Dyche’s side buried in the bottom three, a point adrift of 17th place Everton, while the hosts hit the 30-point mark.
Here are the ratings.
9. Ashley Westwood 5
Perhaps a tad fortunate to be included ahead of Cork, and may not have done enough to retain his place for the meeting with Manchester City after the extended break. While his inviting delivery was squandered by McNeil, his corners failed to hit the money spot, while his distribution became all too predictable as he continued to go long and often. Photo: Julian Finney
10. Maxwel Cornet 6.5
Craving the goal that would give his self-belief a much-welcome and timely boost. Effective when playing off the shoulder, though often took a wrong turn when isolating the final defender. Continued to run the channels, even when starved of quality service, and linked well when getting his foot on the ball. However, wasted two huge chances for the Clarets — one in either half — with the game still goalless. A player of his quality should really have done much better with the second of those chances when getting goal side of Pinnock. Photo: Catherine Ivill
11. Wout Weghorst 5.5
Saw very little of the ball in the first half as Pinnock, Jansson and Ajer stood up to his physicality. Dropped deep to receive the ball into feet in an attempt to influence play, but Brentford's defensive trio successfully forced the Dutchman to play with his back to goal, while dominating the aerials. Ran himself into the ground in his battles for the ball and replaced by Rodriguez after the hour as fatigue kicked in. Photo: Catherine Ivill
12. Jay Rodriguez 6.5
Sean Dyche acknowledged that the striker was rather unfortunate to find himself on the bench, but the Burnley boss was delighted with the substitute's reaction when introduced in the 67th minute. Rodriguez picked up pockets of space to work in, knitting play together nicely, moving the ball out wide, and he deserved so much more when his ambitious and well-hit howitzer bounced back off the bar. Photo: Julian Finney