The Gunners came into the match at Anfield knowing that Manchester City had dropped points at home the day before.
City lost 1-0 to Brighton, their second consecutive defeat in the league.
Arsenal’s winning goal came in the first half of the game, after Declan Rice’s low cross was tapped in by Kai Havertz.
Although the Reds fought to equalise, Mikel Arteta’s men held on strong to keep a clean sheet.
The champions now have 24 points after nine fixtures, three more than City and nine more than Liverpool.
