Odegaard has looked back to his very best in the early stages of the season and that was reflected in the Gunners' latest triumph.
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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.