Albion are lucky to still be level with the Gunners in this first game back since the enforced coronavirus break.
Bukayo Saka came closest to scoring as he rattled the bar, as the visitors looked far sharper than Albion.
Arsenal keeper Bernd Leno was sadly stretchered off after he fell awkwardly in a challenge with Seagulls striker Neal Maupay.
Soon after play restarted Aaron Mooy tested replacement keeper Emiliano Martinez who got down well to save.
Both Alexandre Lacazette and Pieree Emerick Aubameyang have caused Maty Ryan to have to be alert.