A second half brace from Declan Rice made the difference for the Gunners, as the Cherries went to eleven games without a win in the Premier League.
The sides were level at the break after a good start for the Cherries saw them take the lead through Evanilson after an absolute gift from Gabriel Magalhaes as he passed straight to the striker for an easy finish.
Evanilson opened the scoring _(Image: Richard Crease)_
Arsenal drew themselves level as Gabriel redeemed his error at the other end with 16 minutes on the clock.
Rice scored his first of the game nine minutes after the resumption and added his second with 19 minutes to play, both coming in similar fashion as he finished well from a central position inside the box.
Junior Kroupi scored a brilliant goal from range after coming off the bench to get Bournemouth back into it, but they weren’t able to find an equaliser and they were beaten.
Andoni Iraola named an unchanged side from the team which drew with Chelsea, meaning Antoine Semenyo started, as expected, for his 100th Premier League appearance.
Antoine Semenyo _(Image: Richard Crease)_
New signing Fraser Forster was among the substitutes after he joined on a six-month deal yesterday, while Lewis Cook returned to the bench from a neck knock.
The Cherries made an energetic start and had a couple of early corners, but they weren’t able to fashion a clear-cut chance.
The first shot of the game went the way of the visitors as Martin Odegaard blasted over the bar from range, before Noni Madueke did the same when he cut in from the right and should have done better.
But the Cherries took the lead after ten minutes, and Evanilson will not score an easier goal.
Evanilson opened the scoring _(Image: Richard Crease)_
Arsenal were passing the ball around the back comfortably when Gabriel cut the ball across the top of the box, where his countryman was waiting.
The Cherries striker took a couple of touches and passed it beyond the hapless Raya.
Justin Kluivert was not far away as he shot from distance after receiving the ball in a pocket of space outside the box, before Arsenal drew themselves level.
Djordje Petrovic punched well from a free kick, but Madueke beat Semenyo on the right and got to the byline.
He cut the ball back for Piero Hincapie and he and Evanilson went for the bouncing ball but it deflected into the path of Gabriel who powered the ball home at the near post.
Alex Scott _(Image: Richard Crease)_
Bournemouth responded well to the equaliser, and sought to apply the pressure on their visitors.
Marcus Tavernier glanced a James Hill cross wide, before Kluivert was not far away from the bottom corner with a free kick from 30 yards.
Tavernier was on the end of another cross, this time from Kluivert, after he made a run from deep but he couldn’t keep his shot down.
Semenyo shot over the bar after exchanging passes with Evanilson on the edge of the box, as the sides entered the break level pegging.
The Cherries had the first chance of the second half, as David Brooks flashed a shot across goal on the angle after he was played in by a quick free kick from Kluivert.
But moments later, Arsenal took the lead.
Declan Rice netted a second half brace. _(Image: Richard Crease)_
Gabriel Martinelli rose above Hill to head the ball onto Victor Gyokeres, who was dispossessed but the ball fell to Odegaard, and he had time to square it to Rice who finished well into the bottom corner.
The Cherries again responded on the front foot to the Arsenal goal, as Brooks saw a shot blocked behind and Raya saved comfortably from Tavernier.
Iraola went to his bench and introduced Amine Adli in place of Brooks, before the Gunners extended their advantage.
Bukayo Saka was slipped through on the Cherries left and cut the ball back from the byline to Rice for the Englishman to fire into the back of the net.
After three Cherries changes saw Kroupi, Enes Unal and Lewis Cook brought on for Evanilson, Kluivert and Scott, the young French striker got a goal back for the hosts.
Junior Kroupi got the Cherries a goal back _(Image: Richard Crease)_
It was a brilliant strike from range as Tavernier played the ball into Cook who turned it onto Kroupi, and he fired past Raya from outside the box.
Semenyo saw a shot blocked as the crowd rose after the Cherries second, before Mikel Merino saw a shot from distance caught well on the dive by Petrovic.
Gabriel Jesus saw a shot saved by Petrovic after Saka shot high and wide, as the Cherries weren’t able to fashion a final chance to draw level.
Bournemouth remain in 15th on 23 points after 20 games.
**AFC Bournemouth:** 1, D. Petrovic; 3, A. Truffert; 5, M. Senesi; 23, J. Hill; 20, A. Jimenez; 8, A. Scott (Cook 74’); 16, M. Tavernier; 24, A. Semenyo (booked, 27’); 19, J. Kluivert (Kroupi 74’ (booked, 80’)); 7, D. Brooks (c)(Adli, 67’ (booked, 90+1’)); 9, Evanilson (Unal 74’).
**Arsenal:** 1, D. Raya; 5, P. Hincapie; 6, Gabriel; 2, W. Saliba; 12, J. Timber; 41, D. Rice; 36, M. Zubimendi (booked, 70’); 8, M. Odegaard (c)(Merino 80’); 11, G. Martinelli (Trossard 67’); 14, V. Gyokeres (Jesus 67’); 20, N. Madueke (Saka 67’).