Goals from Richarlison and Gylfi Sigurdsson gave Everton their first win at Anfield since 1999 ending their 24-game winless at the Reds and condemning Liverpool to a fourth straight home defeat.
Richarlison opened the scoring inside three minutes with a sharp finish before substitute Sigurdsson made the points safe with a late penalty to seal a famous result and add to Liverpool’s woes.
Carlo Ancelotti’s men came into the game having won just one of the last 28 Premier League meetings with their great rivals but made the perfect start when Richarlison raced through to finish past Alisson.
Liverpool lacked urgency in their play and their challenge became harder when Jordan Henderson limped off with a groin injury, further worsening their problems at centre-half.
Everton, determined in the tackle and brave with the ball, sensed weakness when sending on Dominic Calvert-Lewin from the bench to join Richarlison in attack and it was a gamble that paid off when the England striker won a controversial penalty off Trent Alexander-Arnold.
Sigurdsson rolled home from the spot to seal Everton’s first win against Liverpool since 2010.
Liverpool equal a club record of four successive home league defeats set in 1923 and Everton are now level on points with the Reds in the table having played a game fewer.