David Luiz's first-half header handed Arsenal a 1-0 win over AFC Bournemouth at Emirates Stadium.
The Gunners struck on nine minutes when David Luiz met Nicolas Pepe's corner to score his first goal for the club.
Arsenal had chances to extend their lead with Bukayo Saka's low shot saved and Pierre-Emerick Aubameyang hitting a post late on.
AFC Bournemouth were brighter after the introductions of Ryan Fraser and Arnaut Danjuma, but could not find a way past Bernd Leno.
Arsenal are unbeaten in five Premier League matches and move up to third on 15 points.
AFC Bournemouth drop to 10th with 11 points.
Arsenal: 21 Oct v Sheffield United (A)
AFC Bournemouth: 19 Oct v Norwich City (H)
Referee: Martin Atkinson. Assistants: Adam Nunn, Constantine Hatzidakis. Fourth official: Peter Bankes. VAR: Anthony Taylor. Assistant VAR: Andy Halliday.