Mikel Arteta’s side were already cruising by that point after going 2-0 up before half-time thanks to goals from Bukayo Saka and Odegaard.
Saka nodded home a header from a few years and Odegaard scored a penalty, which had been won by Eddie Nketiah. Arsenal added a fourth in injury-time through Ben White.
Simon Collings was at the Vitality Stadium to see Arsenal in action...
David Raya 7
Didn’t really have masses to do, but was neat and tidy - especially when claiming crosses. Distribution was decent and opened Bournemouth up with one great pass in the first-half.
Ben White 7
Not at his best early on, but improved as the game went on. Got on the scoresheet late on as he headed home from an Odegaard free-kick.
William Saliba 8
Made an excellent tackle early on to deny Dominic Solanke when the striker had been put through and the game was 0-0. Never looked flustered on the ball. A Rolls-Royce of a defender.
Like his centre-back partner, the Brazilian was solid in defence and made some big blocks. Bounced back well after being out of the team earlier this season.
Oleksandr Zinchenko 8
Involved in a lot of Arsenal’s good play and helped win their first penalty by playing in Nketiah. Unlucky not to score on a few occasions.
Martin Odegaard 8 | Star player
A goal and two assists for the captain. Slotted a penalty just before half-time, sending Bournemouth goalkeeper Neto the wrong way. Won the second penalty after being clattered in the box and setup the fourth goal, too.
Declan Rice 8
Another excellent performance at the base of Arsenal’s midfield. Calm in possession and shut down any rare Bournemouth attacks by covering so much ground.
Kai Havertz 7
Off the mark for Arsenal after scoring a penalty. Didn’t look like he was going to take it until Saka handed him the ball. Will hope it is a turning point for him.
Bukayo Saka 7
Opened the scoring by tapping home a header from a few yards out. Concern for Arsenal, though, as he went off limping yet again.
Eddie Nketiah 7
Won the first penalty for Arsenal by linking up well with Oleksandr Zinchenko down the left flank. Started slowly but grew into the game.
Gabriel Jesus 7
So nearly opened the scoring when his header hit the post, but Saka was there to tap in the rebound. Went close again in the second-half when moved up top.
Takehiro Tomiyasu (Zinchenko 69’) 6
On at left-back and was solid for his 20 minutes or so.
Reiss Nelson (Nketiah 69’) 6
A quiet cameo against Bournemouth after his heroics last season.
Fabio Vieira (Saka 76’) N/A
Jorginho (Rice 81’) N/A
Emile Smith Rowe (Havertz 81’) N/A
Subs not used: Ramsdale, Kiwior, Elneny, Trossard