Match ends, Arsenal 1, Bournemouth 0.
David Luiz scored the only goal as Arsenal edged past Bournemouth at Emirates Stadium to move up to third in the Premier League.
Luiz glanced home Nicolas Pepe's ninth-minute corner for his first goal since his summer arrival from Chelsea.
Bournemouth improved after the break and went close through Callum Wilson, but they rarely troubled Bernd Leno in the Arsenal goal.
The Gunners move above Leicester, Burnley and Crystal Palace with the win, while Bournemouth stay 10th.
Pierre-Emerick Aubameyang went close in the opening stages and hit the post late on, but those opportunities bookended a game of few chances.
Bournemouth offered little as an attacking threat, but with Arsenal unable to kill the game off they were able to apply some pressure in the closing stages.
Only a last-ditch tackle from Matteo Guendouzi prevented Joshua King from converting a low cross by Callum Wilson, who also fired straight at Leno in stoppage time.
- How Sunday's Premier League matches unfolded
- Quiz: Name the players to have scored for both Arsenal & Chelsea in Premier League
Arsenal grind out narrow victory
Though they were far from their best, a fourth win of the season means Arsenal go into the international break in the Champions League places having lost just once in eight league games.
But while Unai Emery must be pleased with the way his side battled to the win, he will know there is still room for improvement, with a failure to score a second goal meaning this game was a lot closer than it could have been after their first-half performance.
Emery's side began brightly and went close inside the opening five minutes when Aubameyang fired just wide from the edge of the penalty area after good work by Dani Ceballos and Bukayo Saka.
They did not have to wait much longer to open the scoring, however, with Pepe's corner from the right finding Luiz at the near post, and his flicked header went beyond Aaron Ramsdale into the far corner.
Arsenal thought they had decent claims for a penalty when Pepe went down under a challenge by Diego Rico, but Martin Atkinson waved away the appeals, with his decision upheld following a VAR check.
The Gunners then faded badly in the second half, though Emery cannot blame fatigue as his side showed 10 changes from the 4-0 Europa League victory over Standard Liege on Thursday.
Emery responded by bringing on 18-year-old Gabriel Martinelli for Pepe, who has just one goal in 10 appearances since his club record £72m signing move from Lille in the summer.
Martinelli, who scored two goals in Thursday's win over Standard, showed flashes of quality and fired a curling effort over from just inside the area, but this was an attritional victory rather than one built on attacking flair.
Cherries' woes at Arsenal continue
Bournemouth have found little joy in games against Arsenal, taking just four points from eight meetings and losing all of their previous trips to the Emirates with an aggregate score of 13-2.
There were few positive signs for Cherries fans in the opening period here either, as they rarely threatened the Arsenal backline.
Bournemouth's first opportunity was a Dominic Solanke header from a corner that went well wide, one of just two touches by a Cherries player in the Arsenal penalty area during the first 45 minutes.
To compound matters, Eddie Howe's side also looked vulnerable from set-pieces, with Luiz easily able to escape his marker for the opening goal.
It means the south-coast club remain without a clean sheet this season and have just one shutout in their last 12 top-flight matches stretching back into the last campaign.
That will be of obvious concern to Howe, but he will at least be pleased with the reaction of his players after the break.
They had a decent opportunity early in the second half when Callum Wilson found himself in on goal, but the England striker was drawn wide after rounding Leno and Calum Chambers was able to clear his low cross at the far post with King lurking.
Leno then had to be alert to tip Jack Stacey's cross-shot over the bar after a neat pass from Harry Wilson, while Philip Billing curled an effort wide from distance as Arsenal clung on.
That strong finish will be a positive to take away for the visitors, although Howe will wonder why it took his players 45 minutes to jolt into action.
Man of the match - Calum Chambers (Arsenal)
'We were too passive' - what they said
Arsenal boss Unai Emery, speaking to BBC Sport: "I'm very happy with the result and the first half. We controlled the match and played with a high level, taking chances and scored from a corner. We also didn't concede chances to them and pressed well up the pitch.
"The second half we wanted to keep more of the ball, but they started pushing and maybe we lost our confidence and didn't do the work like we were in the first half."
On the team's young players: "I am being very calm with them. It's very important to keep the balance. When they are playing well keep calm and the same if they are not playing like we want them to. We are there to help them, given them chances and some minutes.
"The Premier League is very demanding and we are going to play a lot of matches like today."
Bournemouth boss Eddie Howe, speaking to BBC Sport: "I'm disappointed with the first half, we were a little bit too passive and didn't dominate our style on them.
"We were second best for long periods. But you saw the other side in the second half, as bad as we were in the first half, we were good in the second.
"We dominated possession and deserved a point, we did well enough and had good enough chances.
"It didn't quite happen but I'm pleased with the reaction to the first half."
Bournemouth lose at one of the 'big six' again - the stats
- Arsenal have won all six of their home matches in all competitions against Bournemouth - only against Gainsborough Trinity (eight wins out of eight) do they have a better 100% home win ratio in their entire history.
- Bournemouth have lost 13 of their last 14 away Premier League games against the 'big six' teams (W1 D0 L13).
- Arsenal have won 17 home Premier League games under Unai Emery. Since the start of last season, only Liverpool (21) and Man City (20) have won more.
- Only against Man City (9) have Bournemouth lost more Premier League games than against Arsenal (7).
- Arsenal have won 14 of their last 17 home matches in all competitions (W14 D2 L1), with this their first 1-0 win in this sequence.
- Bournemouth have won none of their last 25 Premier League matches when conceding first (W0 D5 L20).
- Ten of David Luiz's 12 Premier League goals have been scored in home matches, with this his first goal for Arsenal.
- Nicolas Pepe has been involved in 28 goals in his last 30 home league matches for Lille and Arsenal (16 goals, 12 assists).
Bournemouth host Norwich after the international break on Saturday, 19 October (15:00 BST). Arsenal travel to Bramall Lane to take on Sheffield United the following Monday (20:00 BST).
- 23David Luiz
- 19PépéSubstituted forMartinelliat 63'minutesBooked at 72mins
- 8CeballosSubstituted forWillockat 75'minutes
- 77SakaSubstituted forTorreiraat 83'minutes
- 17StaceyBooked at 29minsSubstituted forFrancisat 79'minutes
- 3S Cook
- 22WilsonSubstituted forDanjuma Groeneveldat 79'minutes
- 29BillingBooked at 13mins
- 9SolankeSubstituted forFraserat 63'minutes
- 14Danjuma Groeneveld
- 16L Cook
- Martin Atkinson
- Shots on Target
Second Half ends, Arsenal 1, Bournemouth 0.
Foul by Pierre-Emerick Aubameyang (Arsenal).
Steve Cook (Bournemouth) wins a free kick in the defensive half.
Attempt saved. Callum Wilson (Bournemouth) right footed shot from outside the box is saved in the centre of the goal. Assisted by Nathan Aké with a headed pass.
Pierre-Emerick Aubameyang (Arsenal) hits the right post with a left footed shot from very close range. Assisted by Calum Chambers.
Corner, Arsenal. Conceded by Jefferson Lerma.
Lucas Torreira (Arsenal) wins a free kick in the defensive half.
Foul by Philip Billing (Bournemouth).
Attempt missed. Steve Cook (Bournemouth) header from the centre of the box is too high. Assisted by Ryan Fraser with a cross following a corner.
Corner, Bournemouth. Conceded by Matteo Guendouzi.
Corner, Arsenal. Conceded by Simon Francis.
David Luiz (Arsenal) wins a free kick in the defensive half.
Foul by Joshua King (Bournemouth).
Foul by Joe Willock (Arsenal).
Arnaut Danjuma Groeneveld (Bournemouth) wins a free kick in the attacking half.
Attempt missed. Arnaut Danjuma Groeneveld (Bournemouth) right footed shot from outside the box is close, but misses to the right.
Substitution, Arsenal. Lucas Torreira replaces Bukayo Saka.
Attempt missed. Gabriel Martinelli (Arsenal) right footed shot from the left side of the box is too high. Assisted by Joe Willock.
Sead Kolasinac (Arsenal) wins a free kick on the left wing.