Fernandinho's late own goal forced Manchester City to settle for a 2-2 draw against Crystal Palace, while Tottenham were held to a goalless draw by Watford.
Manchester City thrashed Aston Villa 6-1 to move ahead of Leicester into second on the Premier League points table.
Man Utd vs Man City: Manchester United face a huge task when the two sides meet again for the League Cup semi-final, second leg on January 29 (local time).
Manchester City vs Everton: Carlo Ancelotti, who has guided Everton to two wins in his first two matches in charge, feels that Manchester City will provide a more realistic barometer on where his side stand.
Man City beat Sheffield United 2-0 on Sunday thanks to second-half strikes from Sergio Aguero and Kevin de Bruyne.
Sergio Aguero played a pivotal role when Manchester City were crowned Premier League champions for the first time in 44 years.
Premier League 2019, Liverpool vs Man City Highlights: Fabinho, Mohamed Salah and Sadio Mane scored for Liverpool, while Bernardo Silva scored Man City's only goal.
Sergio Aguero's double added to struggling Southampton's misery in a 3-1 win for Manchester City.
Man City vs Watford: Bernardo Silva's hat-trick helped Manchester City record their biggest ever top-flight victory.
Brazil coach Tite said he's been having sleepless nights ahead of the Copa America semi-final against Argentina.
Argentina will play in Group B alongside Colombia, Paraguay and guests Qatar, the 2022 World Cup hosts and current Asian champions.
Manchester City remain on course for an unprecedented quadruple of Premier League, Champions League, FA Cup and League Cup.
Manchester City roared back from a two-goal half-time deficit to score three times after the break.
Manchester City demolished Chelsea 6-0 to go top while Tottenham Hotspur cemented their third place with a 3-1 win over Leicester City.
Manchester City's quest for four trophies continued with a 5-0 thrashing of Burnley in FA Cup.
Manchester City recently suffered back-to-back defeats against Crystal Palace and Leicester City.
The win over Everton, moved Manchester City two points ahead of Liverpool, who host Manchester United on Sunday.
Manchester City are now 12 points clear of Manchester United and moved two points ahead of Liverpool at the top.