Manchester clubs, United and City reached the quarter-finals of the Carabao Cup after wins over Brighton and Burnley respectively.
They joined Tottenham Hotspur in the last eight, who had earlier overcome Chelsea.
Meanwhile, the likes of Newcastle United and Everton also won their games to progress.
Three more games are scheduled for tonight.
Here we present the records broken.
As per Opta, Everton, who thrashed West Ham United 4-1, have won each of their opening six games of a campaign for the first time since 1938-39.
James Rodríguez has created 15 chances (including assists) in four games for Everton in all competitions.
This is now the most of any Premier League player in 2020-21 so far.
However, the Frenchman got his maiden goal from a direct free-kick.
Juan Mata has now scored 50 goals in all competitions for Manchester United, including five in the League Cup.
Manchester United beat Brighton twice in four days in all competitions.
Forward Dominic Calvert-Lewin is the first Everton player to score a hat-trick in the League Cup since Paul Rideout versus Lincoln City in September 1993. The Englishman netted his second hat-trick this season in all competitions. He has netted eight goals this season already.
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