Danny Welbeck scored twice as Arsenal bounced back from their heavy defeat to Liverpool with a 3-0 win over Bournemouth on Saturday.
The international break gave the Gunners a chance to reflect on their 4-0 humiliation at Anfield and they produced the perfect response at the Emirates.
Welbeck's early header put them ahead (6) and they deservedly doubled their lead before half-time through Alexandre Lacazette (27).
An excellent finish by the impressive Welbeck completed the scoring for the hosts (50), who move up to ninth in the Premier League table after their second victory of the season.
Arsenal: Cech (7), Bellerin (7), Kolasinac (8), Koscielny (7), Mustafi (7), Ramsey (7), Monreal (7), Xhaka (8), Ozil (8), Welbeck (8), Lacazette (8)
Subs: Coquelin (6), Giroud (6), Sanchez (7)
Bournemouth: Begovic (6), Cook (5), Ake (5), Daniels (6), Smith (5), Arter (5), Mings (5), Gosling (4), Fraser (5), King (5), Defoe (5)
Subs: Francis (6), Ibe (6), Mousset (6)
Man of the match: Danny Welbeck
There was also time for Arsene Wenger to introduce substitute Alexis Sanchez - who was close to joining Manchester City on Deadline Day - and the Chilean received a mixed reception from the home crowd.
Former Schalke man Sead Kolasinac provided the most assists by a defender in the Bundesliga last season and he teed up Welbeck for the opener.
Arsenal were completely dominant, with Asmir Begovic alert to keep out efforts by Granit Xhaka and Mesut Ozil before the hosts added their second. It came courtesy of another fine forward pass by Ozil, who released Lacazette to fire home after a neat exchange with Welbeck.
Alexandre Lacazette and Sead Kolasinac both impressed on their returns to the Arsenal starting XI after the pair missed the 4-0 defeat to Liverpool before the international break.
Little went right for the Cherries, who also lost Ryan Fraser to injury before the break, and they conceded again five minutes after half-time. Dan Gosling coughed up possession and when Ramsey slipped through Welbeck, the Arsenal forward tucked away his second of the game.
Jermain Defoe had struck the post with a header moments before that Welbeck strike, compounding a miserable afternoon for a Bournemouth side still looking for its first point of the campaign.
The visitor's first shot on target did not come until the 85th minute, while the only blot on Arsenal's copybook was a late injury suffered by substitute Francis Coquelin.
- Alexandre Lacazette became only the second Arsenal player to score in his first two home Premier League games for the club, after Marouane Chamakh in 2010.
- Danny Welbeck has scored three goals in four Premier League games this season, having scored just two in 16 appearances in the competition last term.
- Bournemouth have become only the ninth team to lose their opening four games to a Premier League season, though four of the previous eight have managed to avoid relegation.
Man of the match - Danny Welbeck
Bournemouth's back three struggled to cope with Arsenal's attacking threat all afternoon, with Welbeck the main beneficiary.
His tally now stands at four goals from six appearances for club and country, while he also contributed an assist for Lacazette's strike against the Cherries.
He was inches away from a hat-trick too when his audacious second-half chip landed narrowly wide.
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Arsene Wenger: "I feel we played well all over the pitch. It's difficult to single anybody out for a bad performance and overall, if you look at the individual performances, they were all quite good.
"It was a a serious performance, well focused, with a good team discipline and we scored goals and didn't concede. That's what we needed."
On the mixture of boos and cheers for Sanchez, Wenger added: "I don't know why, maybe it is a question of transfers. He will do that [win the fans back] quickly."
Eddie Howe: "We were disappointing from start to finish, we have a lot of work to do.
"If you dip below your levels you get punished, we spoke about that before the game. We were punished today.
"You don't sit on zero points if everything is going great so we will have to dig deep, we will have to really find some character - which we have always shown historically - and we have to bounce back and really show what we are made of."
Arsenal are back at the Emirates on Thursday to open their Europa League campaign against Cologne before returning to league action away to Chelsea on Super Sunday, live on Sky Sports Premier League.
Bournemouth will look to end their four-match losing run in the league when they host Brighton on Friday Night Football, also live on Sky Sports Premier League.