The result means that Liverpool suffered their fourth consecutive defeat in the league and fourth in a row at home.
Liverpool’s dismal day was compounded when they lost captain Jordan Henderson to injury in the first-half
Everton go level on points with Liverpool with both teams three points off the top four places but Everton have a game in hand.
Everton took the lead inside three minutes when James Rodriguez played a through ball to Richarlison who produced an emphatic finish.
The Liverpool captain then limped off just before the half an hour mark with an injury and was replaced with youngster Nathaniel Phillips.
Just before 70 minutes, Mohamed Salah was denied from close-range by another great Pickford save.
With eight minutes remaining, Dominic Calvert-Lewin was brought down by Alexander-Arnold inside the box and Sigurdsson converted the penalty to seal the win.