The Gunners had been hoping to get out of the blocks quickly following their stunning Champions League victory over Lens midweek and Mikel Arteta's side didn't disappoint.
Bukayo Saka gave Arsenal the lead after six minutes, however it was Odegaard's goal just seven minutes later that really got fans talking.
The Norwegian midfielder was on hand to finish off a wonderful team move that saw Oleksandr Zinchenko play a one-two with Gabriel Jesus before playing it to Odegaard, who swept home from inside the penalty area.
Speaking on talkSPORT, Gunners legend Ray Parlour said: "The link-up was absolutely brilliant.
"The touch from Jesus, the ball from Zinchenko was on the button and it was a great finish from Odegaard - the goalkeeper had no chance.
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"What a beautiful goal!"
He wasn't the only person impressed, though, with social media full of compliments for the Arsenal skipper and his teammates as they turned on the style.
The Telegraph's Sam Dean wrote: "Odegaard makes it two and that was a very, very tasty goal. Might just be #AFC's tastiest goal of the season so far."
Another Arsenal fan said: "The free flow by Zinchenko to Odegaard. We're back to the Wenger days."
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A third supporter wrote: "An Odegaard finish just hits differently and is like porn for the the eyes. The man is back cooking."
"Odegaard is our best ball-striker," said another fan. "Earlier this season he was taking his shots 20 yards out. But get him in the box and he's devastating."