The Gunners moved to the top of the fledgling Premier League table, extending their wining run to three games after two goals from their new skipper inside 11 minutes got them off to the best possible start.
Arsenal had to weather a brief Bournemouth storm at the beginning of the second half but any hopes of a comeback were extinguished in the 54th minute when William Saliba curled home an exquisite goal to put the result beyond doubt.
It is the first time in 18 years that Arsenal can boast a 100% record at this stage of a season and with games on the horizon against Fulham, Aston Villa, an out of sorts Manchester United and Everton, expectation is rapidly mounting.
Odegaard, however, insists it would be foolish to get carried away even if the mood could not be more contrasting to 12 months ago when Arsenal lost three straight games and failed to score a single goal.
He said: ‘Compared to last season we are a little bit ahead but we have to stay calm and we have to stay humble and see where it takes us.
It was really solid from start to the end. We came out and dominated, made some good chances and scored some good goals.
‘We know it’s always difficult coming to these places. We have struggled before but we were so sharp and aggressive. It was a good performance from start to finish.’
Odegaard, meanwhile, was quick to note the contribution of Gabriel Jesus who continued his fine form with a sensational all round contribution.
He added: ‘He is not just about goals. He gives us so much in the play and he drops down to combine. He is brilliant and he is amazing to play with. We are lucky to have him here.’
MORE : Nicolas Pepe left out of Arsenal squad to face Bournemouth amid Nice speculation
MORE : Brendan Rodgers confirms why he dropped Wesley Fofana and Youri Tielemans amid Chelsea and Arsenal links
Stay connected with us on social media platform for instant update click here to join our Twitter, & Facebook
We are now on Telegram. Click here to join our channel (@TechiUpdate) and stay updated with the latest Technology headlines.
For all the latest Football News Click Here