The Norwegian sent Arsenal into the lead with a brilliant finish. Odegaard combined well with Kai Havertz, before shooting with his left foot.
Daiki Hashioka's own goal just before half-time saw Arsenal eventually win 2-0 over Luton.
The three points mean Arsenal lead the Premier League by one game more than Liverpool. They play against Sheffield United on Thursday.
– One of the most important breakthroughs in many years (for Arsenal), is the unnerving message from Viaplay commentator Kasper Wickestad.
In a duel: Martin Odegaard and Andros Townsend. Photo: AP Photo/Frank Augustin
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Odegaard's goal was also Drammen's seventh of the season, and 30th overall in the Premier League.
– Spots
Arsenal goalkeepers William Saliba and Gabriel Magalhaes largely contributed to the home side's control of the game, but pundits were a little shocked when they wasted a chance just before the end.
“You almost get nervous when you see Arsenal's goalkeepers make mistakes, because they are so exceptional,” said Viaplay's Lars Tiarnas.
After the match: Thank you to Captain Odegaard for the support. Photography: Reuters/Toby Melville
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Bench stars
Declan Rice and Gabriel Martinelli were on the bench for tonight's key match against Luton. Rice has been one of Arsenal's best players this season and was given a few minutes on the eve of the match.
Another key player – Bukayo Saka – was not in the team. The Briton has recently suffered an injury.
The team made a total of five changes for the match against Manchester City at the weekend, which caused a stir among pundits.
– It could be a cause for concern, said Viaplay expert Tjærnås about the changes.
Worryingly, that apparently did not happen. Arsenal is one point ahead of Liverpool and Manchester City at the time of writing.
The London team will face Brighton away from home on Saturday. Bayern Munich is awaiting a Champions League quarter-final match at home on Tuesday.
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