Manchester United came from behind to beat Everton as Ole Gunnar Solskjaer saw his side secure a much-needed win at Goodison Park.
Roberto Firmino and Diogo Jota were on target for Liverpool, who had fallen behind to a Sander Berge penalty.
Bruno Fernandes scored a penalty with the last kick of an astonishing game as Manchester United stole a 3-2 win over a Brighton and Hove Albion side who struck the woodwork five times.
Rodrigo capitalised on a bad mistake from Ederson to score his first goal for Leeds United and secure a 1-1 Premier League draw against Manchester City at Elland Road.
Sadio Mane scored twice as Kepa Arrizabalaga made another calamitous error in a 2-0 victory for Liverpool over 10-man Chelsea, with Thiago Alcantara conceding a penalty on his debut.
Ben Chilwell produced a star turn on his Premier League debut for Chelsea as Frank Lampard's side beat Crystal Palace 4-0 on Saturday.
Gareth Bale was given a glimpse of the forward line he has joined as Son Heung-min's fantastic four-goal haul and a Harry Kane effort earned Tottenham a 5-2 Premier League victory over Southampton.
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