Liverpool's dismal run continued as they surrended their Merseyside dominance, while Thomas Tuchel's Chelsea were held by Southampton.
Everton claimed their first win at Anfield since 1999 thanks to Richarlison and Gylfi Sigurdsson as Liverpool slipped to another defeat.
Manchester City set a top-flight record in England as they beat Everton to take another step towards the Premier League title.
Richarlison scored twice before Harry Kane forced extra time and Bernard settled a Gylfi Sigurdsson masterclass at Goodison Park.
Edinson Cavani inspired Manchester United to a 2-0 win over Everton in the EFL Cup quarter-final, having clashed with Yerry Mina.
Even without Neymar, Brazil continued their dominance of Uruguay in Montevideo.
Virgil van Dijk could miss the season while Thiago Alcantara is also injured as a result of challenges made by Everton players on Saturday.
Richarlison was sent off for a lunge on Thiago Alcantara in the Merseyside derby and the Brazil forward has apologised for his tackle.
Neymar moved into outright second on Brazil's all-time goalscoring list after a hat-trick against Peru.
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