Burnley became the first team in English top-flight history to lose their first six home games of a season as Crystal Palace earned a 2-0 win at Turf Moor.
Jeffrey Schlupp slid home Jordan Ayew's low cross before half-time following a defensive mistake from Jordan Beyer in Palace's first attack of note in Lancashire.
The hosts deserved to end their losing home run but Johann Berg Gudmundsson, Zeki Amdouni and Jay Rodriguez passed up chances in either half.
- How the teams lined up | Match stats
- Premier League table | Watch free Premier League highlights
- Get Sky Sports | Stream the biggest moments on NOW
As they committed players forward late on they were caught out on the counter-attack as the returning Eberechi Eze teed up Tyrick Mitchell for an injury-time second.
Vincent Kompany's side have now lost all of their home games since their Premier League return to Manchester City, Aston Villa, Tottenham, Manchester United, Chelsea and Saturday's visitors Palace, who rose into the top half after a first win in four league games.
How Eagles heaped misery on Burnley at Turf Moor
Burnley's aims to avoid making history got off to an encouraging start when Amdouni nodded wide from a corner with barely a minute played, and their high-tempo start pegged Palace back in the opening 15 minutes.
But this was not their first false dawn on home soil. As the visitors grew into the game, an all-too familiar defensive slip allowed them in - and they made their hosts pay.
The returning Beyer was too casual in possession and caught out by Ayew, whose unguarded cross was turned home on the slide by Schlupp.
Burnley huffed and puffed before the break, but Gudmundsson's decent header wide and a speculative drive from Amdouni was all they had to show for their endeavour.
The Iceland winger came close again on the hour mark as the hosts continued to press after the interval and should have hit the target when side-footing Amdouni's pull-back wide when unmarked.
Palace were never made to work harder than they would have liked in the hosts' pursuit of an equaliser. Sam Johnstone was only called into action by a long-range Josh Brownhill effort and Jay Rodriguez's header from a corner - in a rare delivery of quality from the home side.
Substitute Wilson Odobert stung the goalkeeper's palms in the dying moments after Kompany shuffled his pack from the bench.
But just as the manager hoped to throw the kitchen sink at their visitors, they were caught out on the counter-attack as Eze fed Mitchell in added time for the left-back's first goal since May 2021, and only the second of his senior career.
That wrapped up victory for Roy Hodgson's side and ensured Burnley's place in the history books for reasons they would never have wished.
Hodgson: We can play better
Crystal Palace manager Roy Hodgson to Sky Sports:
"We can play better than we did, when we did win the ball back we sometimes surrendered it a bit more cheaply than we needed to with the quality in our team.
"Normally in those positions I'd expect more from us. Burnley were good, they put us under a lot of pressure, but it was an outstanding defensive performance and our game management was good.
"Credit to Burnley, they got around the ball very quickly and didn't give us much time."
On Jeffrey Schlupp's opener: "We realised they are good at playing out from the back, they do it well but they do take the odd chance and we hoped we could punish one of the moments when they didn't get it quite right. Jordan chose his moment perfectly, his cross was good and Schlupp did brilliantly to make up the ground to get there."
On Eberechi Eze's return: "It was a difficult game for him, we didn't have the ball as much as we'd like. To get the best out of him, you have to get the ball to him. We didn't get him into the game as much as we would like, but that's the nature of the game."
What's next?
Burnley face a tough test away at Arsenal next Saturday, kick-off 3pm. They then host West Ham after the international break on November 25, kick-off 3pm.
Crystal Palace host Everton next Saturday, kick-off 3pm. They then travel to Bedfordshire to face Luton after the international break on November 25, kick-off 3pm.