Stunning strikes from Bukayo Saka and Thomas Partey and a first Premier League goal for teenager Ethan Nwaneri gave Arsenal a first victory in five league games, reigniting their title challenge.
Arsenal, Premier League runners-up for the past two seasons, started the campaign strongly but their form dipped and they kicked off on Saturday nine points behind leaders Liverpool.
Victory at the Emirates lifts them to 22 points, level with third-placed Chelsea.
Arsenal took the lead in the 15th minute when Saka exchanged passes with Odegaard on the edge of the area before lashing a left-footed shot into the roof of the net.
Captain Odegaard was making his first appearance at the Emirates since late August and showed what a huge miss he was for Arsenal during his two-month injury absence.
Time and again the Norwegian found space in the penalty area with his quick feet and he teed up Gabriel Jesus, who curled narrowly wide, before linking up with Saka again.
Partey doubled Arsenal's lead early in the second half after collecting Saka's pass 20 yards out and taking a touch, before curling his shot away from the dive of Matz Sels and inside the far post.
Seventeen-year-old Nwaneri tucked away Raheem Sterling's cutback to wrap up an emphatic win in the 86th minute.
"I think we started really well," Arteta told the BBC. "The sense I was getting in the last 48 hours after the international break, the boys coming together and were all at it."
Speaking about Odegaard, who returned to action at Inter Milan earlier this month, he said: "It's not a coincidence. The team flows in a different way when he is playing."
And he also had warm words for Nwaneri.
"He is the second-youngest (Premier League goalscorer) in our history," Arteta said. "That's a story in itself.
"He's brave. You see the reaction of fans and they were singing 'He's one of our own'. I think we have to put brick by brick and make sure the cement doesn't get dry. Hopefully we can build a beautiful thing with him."
