Danny Welbeck scored twice as Arsenal returned to winning ways and condemned winless Bournemouth to a fourth successive defeat.
The Gunners came into the game on the back of two costly defeats by Stoke and Liverpool but made the perfect start when Welbeck headed them in front after six minutes.
Record signing Alexandre Lacazette doubled the lead on 27 minutes, bending a shot past Asmir Begovic from the edge of the area.
Welbeck then added a third just after half-time, scoring from a tight angle into Begovic's far corner.
Alexis Sanchez, who was close to joining Manchester City on transfer deadline day, started the day on the bench but came on for Welbeck with 15 minutes remaining.
The Cherries failed to register an attempt in the first half and Jermain Defoe's header against the post after half-time was the best it got for the visitors.
Arsenal were reduced to 10 men for the final 10 minutes when substitute Francis Coquelin was forced off with a hamstring injury but Bournemouth failed to take advantage.
Eddie Howe's side are only off the bottom of the Premier League on goal difference and have lost their opening four games in a season for only the third time.
Arsene Wenger's side were woeful in a 4-0 defeat at Anfield two weeks ago, which followed a 1-0 loss at Stoke.
Then came the final week of the transfer window, which saw a failed bid for Monaco's Thomas Lemar and left the club clinging on to Sanchez, while Alex Oxlade-Chamberlain signed for Liverpool.
The home fans needed a performance and were treated to a clinical one as the Gunners cruised against a poor Bournemouth side.
Wenger set up his team with a back three of Laurent Koscielny, Shkodran Mustafi and Nacho Monreal, who restricted the visitors to just two shots on target in the whole game.
Wing-back Sead Kolasinac led the attacking efforts in the first half, getting forward at every opportunity and providing the cross for Welbeck's opener.
Almost half of Arsenal's play came down the left side of the pitch in the first 45 minutes, while right wing-back Hector Bellerin was crucial to the second half, running down his wing on the counter-attack, tipping the balance in favour of the right.
Mesut Ozil, Granit Xhaka and Ramsey all played like they had a point to prove, while Welbeck and Lacazette started to show signs of a handy partnership.
Such was the performance that Wenger did not need to introduce Sanchez until late in the game and when he did come on, the Chilean looked desperate to get on the scoresheet.
"Sanchez will win the fans back, and win them back very quickly," Wenger said.
The loss of Coquelin on 81 minutes might have usually caused some anxious moments, but Arsenal saw out the game in a professional manner.