Everton, hammered 6-2 at home by Tottenham Hotspur on Sunday, took less than two minutes to grab the lead when the unmarked Yerry Mina headed in a cross from the left by Brazilian winger Bernard.
A curling Lucas Digne free kick beat Burnley keeper Joe Hart to double the lead in the 13th minute and nine minutes later Everton were 3-0 up.
It was the French full-backs third league goal, with his first coming Huddersfield on his home debut.
Burnley defender Ben Mee handled the ball, rising for a header in a crowded penalty area, and referee Michael Oliver awarded a spot-kick which Gylfi Sigurdsson confidently converted.
It was Sigurdsson second goal from the spot this season, the midfielder has now netted two out of four penalties this season.
Sean Dyche's side pulled a goal back eight minutes before the break when a James Tarkowski header was pushed off the line by Jordan Pickford and Ben Gibson hooked the ball home.
But all Burnley's labour towards an attempted comeback came to nothing after Digne made it 4-1 with a low drive from outside the box.
Brazilian substitute Richarlison completed the rout in stoppage time, collecting a fine through pass from Sigurdsson before slipping the ball home.
Richarlison took his tally to nine league goals in 17 appearances.
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