Riyad Mahrez scored for Manchester City as they edged Bournemouth 1-0 while Romelu Lukaku netted a brace for Manchester United in their win over Southampton.
A second-half penalty from Sergio Aguero secured a 1-0 win for City, which stayed a point back in second place.
Former Chelsea captain John Terry and manager Jose Mourinho however, felt that Kepa Arrizabalaga's actions lacked a bit of respect.
Manchester City beat Chelsea 4-3 on penalties to defend their League Cup title after a goalless 120 minutes at the Wembley.
The Manchester United-Liverpool rivalry is the most bitter in all England and United fans know they have the chance to hand a serious blow to Liverpool's ambitions of lifting the Premier League title for the first time in 30 years.
Raheem Sterling scored in the 90th to earn 10-man City a 3-2 win in the first leg of its last-16 match in Gelsenkirchen.
Manchester City's Abu Dhabi ownership has expanded its portfolio of soccer clubs by purchasing Sichuan Jiuniu FC.
"It was the worst conditions I have played in," Foden said. "We had to show professionalism and keep the ball moving and they tired in the end."
Sergio Aguero scored his 11th Premier League hat-trick as Manchester City humiliated Chelsea 6-0 at the Etihad.
Aymeric Laporte and Gabriel Jesus scored for Manchester City during injury time in either half as the visitors went above Liverpool on goal difference.
Liverpool are still top of the Premier League by three points despite being held 1-1 by West Ham on Monday after also drawing with Leicester in the previous game.
As it was, Liverpool's lead is now five points with 14 matches left as the team looks to win the league for the first time since 1990.
Newcastle, the injury-hit and relegation-threatened team, pulled off one of the surprise results of the season by coming from behind to beat Manchester City 2-1.
Kevin De Bruyne scored one and had a hand in two others, with Gabriel Jesus, Bernardo Silva and Sergio Aguero scoring along with an own-goal.
Manchester City moved into the final of the League Cup and will face either Tottenham or Chelsea in the summit clash.
The City manager was unhappy at the pace his team played at, as well as the quality of the passing in the first half.
A deflected 18th-minute strike from Danilo was added to in the second half by wingers Raheem Sterling and Leroy Sane as City eased to a fifth straight win in all competitions.
De Bruyne, Zinchenko, Foden, Walker and Mahrez also scored at Etihad Stadium for a result that virtually renders the second leg meaningless in two weeks.
In other all-English Premier League matchups in Monday's draw, Crystal Palace host Tottenham, and Manchester City will be at home to Burnley.
A year after Liverpool ended City's hopes of emulating Arsenal's 2003-04 Invincibles, the tables were turned on a freezing night that saw the title race open up again.
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