Nathan Collins netted his first goal for the Clarets before Richarlison scored twice from the spot to put the visitors ahead at the interval.
Jay Rodriguez equalised for the hosts and then Maxwel Cornet wrapped up an important three points with the winner five minutes from time.
The win moved Sean Dyche’s side to within a point of the Toffees.
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The win moved Sean Dyche’s side to within a point of the Toffees.
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