Arsenal are through to the last four of Europa League for the second season running after Alexandre Lacazette's fine first-half free-kick settled this tie as a contest.
Napoli created more openings before and after the only goal of the night but Petr Cech was never stretched.
Arsenal is now set for a semi-final encounter with Valencia. Arsenal will host the Spanish team in the first leg on May 2. The second leg will be played on May 9.