The Gunners made it five wins from five in the Premier League after goals from Gabriel Jesus and Gabriel Martinelli ensured they will remain top of the table.
Mikel Arteta's side dominated throughout but looked like they might be left to rue a series of missed chances when Douglas Luiz cancelled out Jesus' opener with 15 minutes remaining.
But Martinelli restored Arsenal's advantage almost immediately, firing in at the back post from Bukayo Saka's excellent cross.
Article continues below
The Gunners now head to Old Trafford on Sunday afternoon for a huge clash with Manchester United.