It was the Toffees’ first defeat of the season.
Premier League champions Leicester are also out after squandering a 2-0 lead to lose 4-2 in extra time with 10 men at home to Chelsea.
Bournemouth were taken to extra time by Championship struggler Preston after a 2-2 draw.
But it was North End who scored the winner in the extra 30 minutes.
No problems for Liverpool and Arsenal who won 3-0 and 4-0 at Derby and Nottingham Forest respectively.
Leeds, Reading and Newcastle also reached the last 16.