The Clarets climbed to eighth in the Premier League and are now just three points off a potential Champions League place after Eddie Howe's Bournemouth were beaten at Turf Moor.
Joshua King and Harry Wilson both had goals chalked off for the visitors following VAR checks while Matej Vydra, Jay Rodriguez (PEN) and Dwight McNeil wrapped up the points as Sean Dyche's side won for the fourth time in five games.
1. Nick Pope 8
Conceded twice against the Cherries, but finished up with a clean sheet. Commanded his penalty area impeccably and made vital stops from Callum and Harry Wilson with the game still goalless.
2. Phil Bardsley 7
Caught out a few times when Smith and King combined in the first half, but got tight to keep the former Rovers man quiet after the break. Puts everything into every ball he goes in for, though was booked for a mistimed challenge on Billing.
3. Charlie Taylor 7
Always busting a gut from full back to provide the overlap and offer his team-mates an option down the left hand side. Manages to get beyond the opponent's right back time and time again to feed the ball into the box.
4. James Tarkowski 8
Another standout performance from the Burnley centre back. Showed a cool head in some pressurised situations at the back, won everything he competed for and made a key intervention to deny King early in the first half.