Morgan Rogers broke the deadlock inside 77 seconds, making Chelsea the first team in Premier League history to score inside the opening five minutes of each of their first three matches this season.
Havertz levelled shortly before the half-hour mark, beating Emi Martínez at his near post after the ball ran through the legs of Maxence Lacroix, before Odegaard struck moments after the restart to complete the turnaround.
The winning goal stemmed from a defence-splitting pass by Christos Tzolis, who cut inside before threading the ball into Havertz. With neither Romeo Lavia nor Reece James tracking his run from midfield, the Arsenal captain feigned a touch, allowing the ball to run into Odegaard's path for the Norwegian to finish emphatically.
Speaking to Sky Sports afterwards, Odegaard was quick to credit his forward for the movement that created the opening.
"He's a really smart player, he moves so well and takes a lot of attention from the defenders, and it was a brilliant goal," Odegaard said.
He also reflected on the significance of the win itself.
"It was a big game, massive game, tough opponent, and we got there in the end, so brilliant. Our mentality is to keep fighting. We have shown that many times. We never want to concede early, but the reaction is top. We got our reward in the end, and the response was brilliant. We showed our quality with and without the ball, and the result reflects that."
Havertz returned the compliment in a separate interview with Match of the Day, praising his captain's continued excellence.
"I think he's an unbelievable player, we saw that over the last years. This season, I think he's back to his best. I think he's going to help us a lot this season," he said.
The forward was also pleased to have got the better of a London rival.
"It's always nice to win at home against a London rival. It was a tough game, but over the 90 minutes, we deserved to win that game," Havertz said, before addressing the challenge of containing Chelsea's attack.
"They have strong players. They have an amazing squad, but so do we. We knew it was going to be tough, and it's going to be a tight game. They scored early, so it's not easy for us, but we believed in ourselves and changed the game around."
Reflecting on his own finish, Havertz credited a slice of fortune for the way the chance fell to him.
"I was happy the ball went through the legs of the defender, so it was tough to see the ball for him. Always happy to score," he said.