With both sides chasing places in Europe next season, it was Carlo Ancelotti's side who came out on top with a first win in seven games.
German keeper Leno turned a Richarlison cross into his own goal in the 76th minute to give the Toffees victory.
Arsenal supporters had gathered outside the ground demanding Kroenke stand down after the club's attempt to join the doomed Super League project.
The result left Everton in eighth place, three points off the Champions League places.
Arsenal are ninth, nine points off the top four.
Standout matches today