A dominant second half display from Arsenal kept the Cherries at bay as Bournemouth's winless run is pushed to eleven games.
Andoni Iraola named an unchanged team from their 2-2 draw with Chelsea earlier in the week which included Antoine Semenyo making his 100th Premier League appearance amid his pending move to Manchester City.
Mikel Arteta on the other hand made three changes, including both wingers as Madueke and Martinelli replaced Trossard and Saka as well as Merino being replaced by Rice who was returning after a small injury absence.
A packed Vitality Stadium was well up for the match against the league leaders, hoping to see the Cherries end their ten-game winless run.
The Cherries started the game in true Iraola fashion and worked themselves a corner in just 20 seconds before piling more early pressure on the visitors.
It didn’t take long for Arsenal to show why they were top of the league however, winning the ball back and calming the game down with their possession based football.
A gift from Arsenal’s Gabriel gave the Cherries the opener just ten minutes in after his thoughtless pass ended up straight at Evanilson’s feet which gave the striker a near open goal to put Bournemouth ahead.
He made up for it just six minutes later however, a few scrappy blocks in the Bournemouth box left Gabriel with the ball at his feet and he powered it past Petrovic to square the game.
Both teams went back and forth for much of the first half, Marcus Tavernier had a good chance to put the Cherries back in front from a Justin Kluivert cross but didn’t connect properly with the ball.
It remained 1-1 as the teams headed down the tunnel for half time and Bournemouth were holding their own against the league leaders.
Mikel Arteta’s side controlled the opening exchanges of the second half, seemingly trying to slow the game down to their own pace.
It then took just 8 minutes for Arsenal to take the lead for the first time in the game, Gyökeres’ hold up play allowed Ødegaard to find Declan Rice on the edge of the box who calmly slotted the ball into the corner of Petrovic’s net.
Arsenal took control for much of the second half, keeping the ball well and limiting the chances Bournemouth were able to create.
They then gave themselves a two goal cushion, 71 minutes in, when substitute Bukayo Saka cut past Truffert and put it on a plate for Rice who again passed into the Bournemouth net for his second of the game.
Just two minutes after entering the pitch Junior Kroupi pulled a goal back for the Cherries with 15 minutes to go, striking wonderfully from outside the box and past David Raya.
Bournemouth pushed for an equaliser but the visitors stood strong and had a handful of chances themselves for a fourth of the game.
The final whistle made it eleven games without a win for the Cherries and now host Tottenham back at Vitality Stadium on Wednesday evening.