Chelsea stole the headlines with a 6-0 win over Barnsley.
Arsenal beat Leicester City, whereas, Everton dished out a 5-2 defeat on Fleetwood.
Newcastle scored seven against Morecambe.
Here we present the key numbers from the matches.
Chelsea, who bought Kai Havertz in the summer for a staggering 71m, saw the German international net a hat-trick.
This was Havertz's first hat-trick of his senior career, in what was his 153rd appearance for Bayer Leverkusen/Chelsea.
Havertz has now been involved in 26 goals in all competitions in 2020, scoring 18 and making eight assists.
Arsenal have maintained a 100% start this season.
After winning the Community Shield trophy, they sealed successive Premier League wins and now earned a crucial 2-0 victory against Leicester.
After losing three successive away games against Leicester in all competitions, the Gunners recorded a win.
Meanwhile, Christian Fuchs' own goal was the first Arsenal have benefited from since April 2019 against Napoli.
Everton registered their third successive victory this season in all competitions.
The Toffees have scored five-plus goals in consecutive matches in all competitions for the first time since September 1964.
As per Opta, Alex Iwobi has both scored and assisted a goal in the same match for the first time in what is his 180th senior appearance in English football.
This was the first time Newcastle scored five first-half goals in a single match since they led Leicester 6-0 at half-time in the second tier in May 1993.
Miguel Almiron has both scored and assisted a goal in the same game for the first time for Newcastle.
Joelinton has now scored three goals in eight cup appearances for the Magpies.
Meanwhile, three more matches are still to be played tonight in the third round of the EFL Cup. Bristol City face Aston Villa, Lincoln City welcome Premier League champions Liverpool, whereas, defending champions Manchester City face Bournemouth.
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