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.