Report Gunners target Gonzalo Higuain, who swapped Real Madrid for Napoli this summer, was named among the substitutes for the Italian outfit, but another new signing Jose Callejon was among the starters for the away side.
A mistake from Carl Jenkinson allowed Napoli to take the lead after seven minutes, however, with Lorenzo Insigne collecting a loose header from the Gunners defender before firing his effort into the bottom corner.
Reina presented Gnabry with a half-chance after 14 minutes following a poor clearance, but the youngster could only find the top of the net with his floating effort.
Napoli had a penalty shout of their own moments later, but the referee was not interested despite Gibbs seemingly committing a foul on Goran Pandev inside the box.
However, Pandev made up for that disappointment with a goal, curling a fine effort into the top corner just short of the half-hour mark.
Insigne had another chance in the latter stages of the half, but the Italian's effort moved just wide of the post before Podolski fired off target at the other end.
Jack Wilshere had a fine chance to cut the deficit for Arsenal in the early stages of the second period, but the England midfielder could only turn his effort wide of the post.
Olivier Giroud and Podolski both had half-chances for the Gunners just before the hour mark, but neither could find a way past Reina in the Napoli goal.
Arsenal did open their account 18 minutes from time, however, when a bicycle kick from Giroud ended up in the bottom corner, albeit via a deflection from Bacary Sagna.
The Gunners, who increased the tempo in the final stages, eventually found the equaliser in the 86th minute when Laurent Koscielny headed home from close range.