Arsenal captain Martin Odegaard bizarrely marked James Tarkowski, who scored the only goal in Saturday's lunch-time game.
Everton picked up just their fourth win of the season as they climbed out of the Premier League relegation zone.
James Tarkowski, who was managed by new boss Sean Dyche at Burnley headed in the only goal of the game on the hour mark to dent the Gunners' title hopes.
The 30-year-old defender overpowered Odegaard at the back-post to guide the ball in the far-post on the hour mark.
It was just exactly what Sean Dyche was hoping for on his first game in charge of the Toffees, who have now beat Arsenal at home in three consecutive seasons.