Burnley went sixth in the Premier League table as they extended their remarkable unbeaten away start at Goodison Park.
The Clarets claimed their first win at Everton since 1976, as they made it five unbeaten in the top flight for the first time since 1974/75 with Jeff Hendrick’s goal midway through the first half.
Burnley, remarkably, now have more points and wins on the road than in the whole of last season.
Everton had a number of early openings, as Burnley caused their own problems defensively.
Oumar Niasse fired straight at Nick Pope after Dominic Calvert-Lewin was allowed time to turn on the edge of the box, while Gylfi Sigurdssson’s effort was well saved, after Ben Mee tried to control a clearance, and Calvert-Lewin and Nikola Vlasic carves out the opening.
Stephen Ward had to clear for a corner, as Niasse lifted a Vlasic flick on over a stranded Pope, while James Tarkowski was forced into a superb block on edge of area from Niasse.
However, once Burnley got the ball down and started to play, they began to dominate proceedings.
Jordan Pickford prevented a deflected Matt Lowton cross from finding Chris Wood, before a glorious opener.
Every outfield player bar Mee was involved as the Clarets strung together 24 passes, Robbie Brady switching play for Scott Arfield to find the run of Ward, and from his pull back, Jeff Hendrick showed great composure to create a yard and fire home.
Only Manchester City have carved out a Premier League goal with more passes involved so far this season - a superb example of the evolution of Sean Dyche’s Burnley.
Idrissa Gueye sliced an effort well wide at the other end, before Pickford claimed Wood’s header from a Pope free kick.
Niasse also slashed a shot wide, before Ashley Williams’ clearance hit Wood, and with Arfield poised to pull the trigger, he went down under the slightest of contact from the Wales skipper.
Arfield was booked for simulation, but it looked a case of no foul, and no dive.
Boos greeted the half-time whistle from the disgruntled home fans - music to Burnley’s ears.
Everton upped the pressure after the break, but Burnley had the best opening as Wood and Brady combined, the latter having a shot beaten away by Pickford at the near post.
Calvert-Lewin headed Cuco Martinez’s cross wide of the near post, and Wayne Rooney was introduced at the expense of Morgan Schneiderlin.
Rooney demanded a penalty as the ball hit Lowton’s hand in the area, but referee Jon Moss was unmoved, and Calvert-Lewin had a decent opening saved at the near post by Pope, after a Rooney pass inside.
But Burnley saw out the game with little fuss, to claim another impressive away result.