Pep Guardiola's side earned their second win in four games as Arsenal suffered their second loss this campaign.
Raheem Sterling's goal was the difference in this 1-0 victory for Man City.
Earlier, Everton held Liverpool 2-2, whereas, Chelsea were held by Southampton 3-3.
Here are the records broken.
Sterling, who was made captain by Pep Guardiola, scored from the rebound after Phil Foden's 23rd-minute shot was saved.
City goal-keeper Ederson denied Arsenal with three excellent first-half saves.
Meanwhile, both David Luiz and Nicolas Pepe were off target with free-kicks in good positions.
Pep is yet to drop a point against Arsenal in five encounters at the Etihad since he succeeded Manuel Pellegrini.
According to Opta, Arsenal have lost each of their last seven league games against Manchester City.
This is their longest such run against an opponent since losing seven in a row versus Ipswich between 1974-1977.
City talisman Raheem Sterling has been directly involved in six goals in his last five Premier League appearances against Arsenal (four goals, two assists).
The Saints have lost just one of their last eight away league games as Chelsea have lost just one of their last nine home EPL games.
As per Opta, Timo Werner and Kai Havertz became the fifth and sixth German internationals to score for Chelsea in the Premier League.
Liverpool are unbeaten in their past 23 meetings against Everton in all competitions.
The Merseyside derby has seen more red cards than any other fixture in Premier League history (22).
Liverpool have conceded 13 goals in their five league games this season.
Mohamed Salah scored his 100th goal for the Reds in all competitions.
Sadio Mane registered the fastest Merseyside derby goal in EPL.
As per Opta, Dominic Calvert-Lewin became the first player to score in each of Everton's first five league games in a season since Tommy Lawton (1938-39). He is just the fourth player to score in each of the first five EPL games in a season.
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