Chris Wood's late header from a corner completed Burnley's comeback having fallen behind at Turf Moor.
Cenk Tosun scored his first goal for Everton to put the Toffees ahead, a neatly finished header beating Nick Pope at the near post.
Sean Dyche's side then took advantage of their superiority as Ashley Barnes latched onto a wonderful through ball and smashing home the finish to level things up. Chris Wood then put the hosts in the lead with ten minutes to play, planting a powerful close-range header past Jordan Pickford which proved to be decisive.