Odegaard has looked back to his very best in the early stages of the season and that was reflected in the Gunners' latest triumph.
The Norway star netted the winner early in the second half with a composed finish after a clever dummy by teammate Kai Havertz.
Odegaard, who notched a 9.1 player rating, also created two big chances from four key passes and recorded a game-high eight progressive passes.
Arsenal's attention turns to the Champions League when they begin their campaign with a trip to Napoli on Wednesday.
They then return to Premier League action on Saturday away to Sunderland.