Xherdan Shaqiri scored twice to bail out Alisson after a first-half howler to secure Liverpool a 3-1 win over bitter rival Manchester United at Anfield, lifting the Reds back to the league lead.
Manchester United manager Jose Mourinho has left the Premier League club after less than three seasons.
Charlie Austin gave Ralph Hasenhuttl his first victory in charge of Southampton and ruined Arsenal's 22-game unbeaten run with an 85th-minute winner in a 3-2 triumph.
Eden Hazard starred for Chelsea as he scored one and set up another in a hard-fought 2-1 Premier League victory over Brighton and Hove Albion.
Chris Smalling's Manchester United career is set to continue for the long-term after he signed a new contract with the club.
Christian Eriksen struck in injury time to give Tottenham a 1-0 Premier League victory over Burnley on Sunday (AEDT).
EXCLUSIVE: Manchester United manager Jose Mourinho conceded his team was taken aback by Liverpool FC's intensity, before conceding there was an element of luck with Xherdan Shaqiri's two late goals.