Liverpool kept pace with Manchester City at the top of the Premier League as two second-half goals gave them a victory that deepens Merseyside rivals Everton's relegation worries.
Andrew Robertson's header broke the visitors' resistance and Divock Origi's finish sealed the crucial points.
It means the Reds stay a point behind league-leaders Manchester City.
Everton's loss, coupled with Burnley's win over Wolves on Sunday, means they drop into the bottom three.
Frank Lampard's side are two points behind the Clarets and have a game in hand but face a big challenge to maintain their top-flight status, with games against Chelsea and Leicester next up.