Jack Grealish scored a dramatic 93rd-minute winner as Everton came from behind to end Crystal Palace’s club-record 19-match unbeaten run.
Daniel Munoz’s tidy 37th-minute finish put in-form Palace on course to make it three Premier League wins in a row – as well as three straight league wins on the road.
Everton were second best for long spells, with Tyrick Mitchell firing against a post before Munoz scored for the second consecutive game.
Ismaila Sarr picked out the Colombia left-back in space on the right side of the box, with Munoz poking past Jordan Pickford, who was making his 300th Premier League appearance for Everton.
The Toffees, who replaced teenager Tyler Dibling and Thierno Barry at the start of the second half, played with a better tempo after half-time.
And they equalised in the 76th minute when Iliman Ndiaye scored from the spot after a clumsy challenge by Maxence Lacroix on substitute Tim Iroegbunam.
The game looked to be heading for a draw when Grealish, who is on loan from Manchester City, scored his first goal in a Toffees shirt after Beto’s header was saved at point-blank range by Dean Henderson. This was Palace’s first defeat in all competitions since 16 April.
Crystal Palace fans have already enjoyed Conference League trips to Norway and Poland this season, but it is eight years since Everton last competed in Europe.
The Toffees remain a work in progress under David Moyes but there is compelling evidence they are moving in the right direction under the Scot with this comeback win greeted with huge celebration among the home support. They were poor for long periods against a Palace side who should have had the game won before Ndiaye equalised from the spot after Lacroix’s needless challenge.
That goal lifted the home side who won it through Grealish in the most dramatic fashion.
Grealish, playing his final game for three weeks as he is ineligible to face parent club Manchester City in Everton’s first game back after the international break, has already proved his worth with four Premier League assists since arriving.
Moyes mentioned in his pre-match news conference that he wanted to see his number 18 score more, and Grealish answered with his first Premier League goal since 2 April to seal Everton’s first league win since August.
Crystal Palace have never had it so good.
The FA Cup and Community Shield gleaming in the trophy cabinet, wins home and away in Europe.
But they will be unhappy with the circumstances that led to the end of their long unbeaten run.
At 1-0, Jean-Philippe Mateta had a goalbound attempt headed off the line while the French forward had other opportunities to score before he was surprisingly replaced by Eddie Nketiah in the 70th minute.
Palace have coped with juggling the demands of Thursday-Sunday European and Premier League football – they drew against Nottingham Forest and won at Aston Villa after their previous two European matches.
But after winning against Dynamo Kyiv in Poland in midweek, this was one game too much for the Eagles.
Everton will return from the international break to play Manchester City at Etihad Stadium on Saturday, 18 October (15:00 BST).
On the same day, Crystal Palace welcome Bournemouth – who have also started the season well – to Selhurst Park for a 15:00 kick-off.