Sam Vokes has scored in consecutive Premier League appearances after netting just once in his previo
Scott Arfield's 90th-minute winner gave Burnley their third win of the season in a match dominated by Everton at Turf Moor.
It had looked like Yannick Bolasie's first Everton goal had earned his side a point before Arfield fired home after Johann Berg Gudmundsson's fierce shot rebounded off the crossbar.
Kevin Mirallas nearly gave the visitors an early lead but an error by Everton keeper Maarten Stekelenburg allowed Sam Vokes to poke Burnley in front.
Bolasie stole the ball off team-mate Romelu Lukaku before firing across home keeper Tom Heaton to equalise.
Lukaku was twice close to making it 2-1 to the Toffees but Michael Keane and Heaton both made crucial clearances with the Belgium striker ready to pounce.
It is Everton's second league defeat under manager Ronald Koeman.
