Arsenal missed the chance to go top of the Premier League as Everton came from behind to secure a first victory since October.
The Gunners, who had won their previous three games, were rewarded for an impressive start as Alexis Sanchez’s free-kick deflected in off Ashley Williams.
Everton equalised just before half-time when Seamus Coleman glanced home Leighton Baines’ excellent cross.
The Toffees, encouraged by a vocal crowd, dominated thereafter and Williams powered home a late header to complete the turnaround.
Home captain Phil Jagielka was sent off in the dying minutes for a second bookable offence and Arsenal had two shots cleared off the line in a frantic finale.
But they could not prevent a first league defeat since their opening match of the season, leaving them three points behind leaders Chelsea, who have a game in hand.
Everton, meanwhile, are up to seventh, four points behind fifth-placed Tottenham.
Arsenal had thumped West Ham 5-1, Basel 4-1 and Stoke 3-1 in their previous three games, but two away games in the space of five days at Everton and Manchester City would provide Arsene Wenger’s side with a real chance to prove they are genuine title challengers.
After Sanchez struck, and with the hosts struggling to get out of their own half, it looked as though another big win was on the cards. But the Gunners failed to build on the goal, which came from their only shot on target until the 90th minute, when Nacho Monreal and Alexi Iwobi had efforts cleared off the line.
It may just have been an off day for Arsenal’s forwards, but they are also struggling at the other end.
Wenger’s men have failed to keep a clean sheet in 11 successive games, and the Frenchman must address that if they are to challenge for a first league title since 2004.
The scrutiny on Everton boss Ronald Koeman had increased during a run of just one win in the 10 Premier League games prior to Arsenal’s visit.
They had also kept just one clean sheet in that time and, against a free-scoring Arsenal, they were cautious from the outset.
For the first quarter of an hour there was a significant gap between forwards Romelu Lukaku and Enner Valencia and their team-mates, as they looked to play on the counter-attack.
It was an ineffective tactic as they failed to trouble Petr Cech, but Sanchez’s goal forced them to become more adventurous. The midfield pushed up to offer Lukaku and Valencia more support, and they suddenly looked a more dangerous side.
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