Demarai Gray's superb injury-time strike earned Everton a first win in nine games to end a bruising week with a stunning comeback against Arsenal.
After a week in which the hosts were thumped by Liverpool and director of football Marcel Brands left the club, Rafael Benitez's team responded with a much-improved display that showed the character and resilience fans were looking for.
Richarlison had brought Everton level with 10 minutes of normal time remaining after Martin Odegaard scored the game's opener from Kieran Tierney's cross in first-half stoppage time.
That the winner came after Richarlison had also had two goals ruled out for offside by the video assistant referee before getting the equaliser will only have added to the home fans' delight.