The visiting side found an early goal with Richarlison de Pedro Andrade in the third minute at the Anfield stadium in Merseyside county.
Everton doubled the lead in the 83the minute as Icelandic midfielder Gylfi Sigurdsson successfully converted a penalty kick for his team. Liverpool faced their fourth consecutive Premier League defeat as the Reds lost four consecutive home league matches for the first time since 1923.
The Reds are in sixth spot with 40 points, whereas Everton increased their points to 40, securing seventh place on matchday 25.
