Everton took the lead after 22 minutes when former Arsenal forward Alex Iwobi crossed the ball into the box where it bounced off the head of Dominic Calvert-Lewin and then Holding before entering the net.
Arsenal levelled on 35 minutes when Tom Davies brought down Ainsley Maitland-Niles in the box and a penalty was awarded. Pepe sent Jordan Pickford the wrong way before placing the ball in the bottom left corner.
Arsenal improved in the second half but were unable to find a score to level the game.
The result puts Everton second in the table while Arsenal remain in 15th.