Sean Dyche's side will now play in the top flight for a sixth successive season thanks to goals from Ashley Westwood and Chris Wood
Westwood broke the deadlock in the 35th minute when finishing Matej Vydra's pass from the penalty spot.
Wood then netted his eighth goal in as many games with a thunderbolt, turning on Josh Brownhill's pass and picking out the top corner.
5. Ben Mee 7.7
Captain fantastic. Mitrovic, Decordova-Reid, Lookman or Cavaleiro didn't get a look in and the skipper stood in their way without breaking a sweat. Whether the threat came from out wide, through the middle, high ball, low ball, Mee dealt with it stoically.
6. Josh Brownhill 7.3
The midfielder put in a real shift down Burnley's right hand side. The former Bristol City man should have a movie named in his honour - "The Interceptor". Battle hardened in the middle of the park and claimed an assist for Burnley's second.
7. Dwight McNeil 6.8
Things didn't quite go his way at Craven Cottage, but he stuck to the task and kept trying to make things happen. Worked hard against the ball, preventing Tete from getting forward while allowing Taylor to advance. Showed plenty of heart.
8. Jack Cork 7.4
Cool and composed in midfield, taking the sting out of the game when needed. Protected the ball well, allowing his team-mates to readjust, and economical in possession. Turned the ball over, helping the Clarets get on the front foot.