The Gunners were two goals down inside the opening 12 minutes through an Ilkay Gundogan header and Ferran Torres' strike, before losing Granit Xhaka to a straight red card for a reckless challenge.
Gabriel Jesus and Rodri added to City's goals tally either side of half-time and Torres rounded off the scoring in the closing stages with his second of the contest.
Arsenal has now lost its opening three league games without scoring and remains in the relegation zone, while City has recovered from its opening-game defeat to Tottenham Hotspur with back-to-back wins without conceding.
After putting five unanswered goals past Norwich City last weekend, the hosts named an unchanged starting line-up in the league for the first time since October 2017 and soon picked up from where they left off.
Bernardo Silva and Jesus combined down the right and the latter sent a cross to the back post for Gundogan to head past Bernd Leno before the Arsenal goalkeeper could properly react.
That was the 10th time in a row City had opened the scoring against Arsenal in the league and it soon had a second goal thanks to Torres' simple finish after Silva's cross somehow made its way through to the unmarked Spaniard.
The goal was allowed to stand after a video assistant referee (VAR) check for a possible foul on Calum Chambers and Arteta, having also seen Kieran Tierney denied a penalty, had further reason to be annoyed when Xhaka was sent off for lunging in on Joao Cancelo.
Jesus tapped in a third goal for City shortly before half-time after being teed up by Jack Grealish at the end of a flowing move and Rodri sided-footed a fourth past Leno from further out eight minutes after the restart.
Substitute Raheem Sterling was twice denied by Leno after being introduced from the bench, but Torres, who had set up Rodri's strike, converted a Riyad Mahrez cross with a header in off the post to register a third successive 5-0 home win for City in the Premier League.