It is surely too early in the season to get carried away, and there are likely to be bigger tests ahead for Mikel Arteta’s side.
But Arsenal have set down an early marker as they chase back-to-back Premier League crowns.
Along with Manchester City, they are one of only two clubs with a maximum nine points from three games.
After sweeping aside Coventry on the opening day of the season, they produced a mature performance to come away with all three points at Villa.
Against Chelsea, they had to find a different way to win after £117m signing Rogers fired Chelsea into a second-minute lead.
“Our mentality is to keep fighting. We have shown that many times,” said captain Odegaard, who scored the 50th-minute winner after Havertz had equalised before half-time.
“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.”
Odegaard has scored three goals in four appearances in all competitions this season, after netting only once in 36 last term.
“It was a big game, massive game, tough opponent, and we got there in the end, so brilliant,” he said.
Former Manchester United and England player Ashley Young said Odegaard’s form will be key for Arsenal this season.
“He’s just a joy to watch,” Young told BBC Sport.
“He’s exciting when he gets on the ball, he’s allowing other players to get on the ball.
“The connection down the right side between him, Bukayo Saka and Havertz – it’s just good to see when you’ve got players that know each other and build relationships in that way.
“Riccardo Calafiori has been brilliant from last season. He seems to me like he’s the one that’s got a free role in the team.
“It was his run, and he played it precisely, for the winning goal. He goes quickly, takes people out of the way. It’s just clever. Arsenal deserved all three points.”
Havertz said Odegaard was back to his “very best”.
“He’s an unbelievable player – we have seen that over the last years,” said the Germany forward.
“He’s going to help us a lot this season.”