Jeff Hendrick increased the pressure on Everton manager Ronald Koeman with the only goal in a 1-0 win for Burnley at Goodison Park.
The midfielder finished a flowing, passing move in the 21st minute of the Super Sunday clash to leave Everton in 16th, two points above the relegation zone, ahead of the international break.
The win means Burnley have picked up eight away points this season - more than they managed in the whole of the previous campaign - despite playing Chelsea, Tottenham, Liverpool and Everton in those fixtures.
However, Koeman - who was tipped for the sack by some of the Sunday newspapers if he lost this game - saw his side suffer their fourth loss in seven Premier League matches so far, despite the second-half introduction of Wayne Rooney from the substitutes' bench.
Everton actually started well, Gylfi Sigurdsson shooting straight at Nick Pope with a presentable early chance and Oumar Niasse also forcing a save from the Burnley goalkeeper, before the visitors opened the scoring with a 24-pass move involving nine players.
After some tidy build-up play, Stephen Ward cut the ball back to Hendrick near the penalty spot and he took a touch past Morgan Schneiderlin before rifling low past Jordan Pickford.
Burnley ended the first half on top and wanted a penalty when Scott Arfield went down under a challenge from Ashley Williams - but the midfielder was correctly booked by referee Jon Moss for simulation.
When Niasse headed Everton's first chance of the second half wide of Pope's goal in the 63rd minute, Koeman responded immediately by introducing Rooney for Schneiderlin, before Tom Davies came on to replace the ineffective Nikola Vlasic six minutes later.
But it was Burnley who carved out the best chance of the second half, as Pickford was forced to block Robbie Brady's cross across the six-yard box with Chris Wood hoping for a tap-in.
And despite long-range efforts from both Rooney and Davies in the closing stages - and an injury-time penalty appeal which struck the chest, rather than hand, of Matt Lowton - they rarely looked like scoring and the home fans booed the players off the pitch.
Opta stats
- Everton have already lost as many league games at Goodison Park this term as they did in the whole of Koeman's first season at the club (2 in 2016/17).
- There were 24 passes in the build-up to Burnley's opener; the second-most for a Premier League goal in 2017/18 (after Fabian Delph v Crystal Palace - 31).
- Hendrick's goal also featured the most passes in the build-up of any Burnley goal in Premier League history (24).
- Burnley pair James Tarkowski and Ben Mee have made more blocks between them (30) than 16 of the other 19 Premier League teams this season.
The managers
Ronald Koeman (Everton): "We started the game really well, we played aggressive, we were playing a total game and the better team. The first shot on target is a goal for Burnley. If you analyse the Burnley team it then becomes really difficult. You have a lot of possession but they are strong and organised defensively. You need to be at your best."
Sean Dyche (Burnley): "I know there is a bit of noise about how they are playing and their tricky start but they have some very good players. We didn't come here thinking remotely it would be an easy game and I thought our lads dealt with that very well. We had a bit of a soft start but we grew into the game and scored a great goal. It was a fantastic bit of play. We can play when we need to and I think we can play longer and stronger when we have to as well."
Man of the Match - James Tarkowski
Many may have feared for Burnley defensively when Michael Keane left for Everton over the summer, but 24-year-old James Tarkowski has filled the void superbly. Not only is he an ultra-reliable defender - he made 12 clearances, four tackles and three blocks in the game - but his passing statistics were superior to any of his team-mates.
Sky Sports co-commentator Andy Hinchcliffe said: "It has to be James Tarkowski. Michael Keane's departure gave him a chance and he really has taken it. It's been an outstanding, individual defensive display. He was rock-solid, giving Burnley a defensive platform and that's exactly what you need away from home playing this way." Sean Dyche appears to have unearthed another gem.
What's next?
After the international break, Everton travel to Brighton on Sunday October 15, while Burnley are next in action 24 hours earlier at home to West Ham.