A fast-paced start from the Gunners was rewarded with a strike from Aaron Ramsey 14 minutes in, followed up by an own goal from Kalidou Koulibaly after he got in the way of Lucas Torreira's off-target shot.
The hosts had chances to score a third and effectively kill off the tie, but a below-par Napoli also occasionally threatened without scoring the crucial away goal they were after, meaning there is still plenty riding on next week's return match.
Arsenal made five changes on the back of their 1-0 loss to Everton last weekend. Ramsey and Pierre-Emerick Aubameyang were among those to return, joining Alexandre Lacazette and Mesut Ozil in an attack-minded XI - Unai Emery knowing the importance of picking up a victory on home soil.
Napoli had Premier League-linked defender Koulibaly in their ranks, and the Senegalese centre-back showed why he is so highly rated when getting in the way of quickfire shots from Ramsey and Ainsley Maitland-Niles early on.
The Gunners were the side on top in the opening 15 minutes, and their pressure told when Ramsey found a way through for the opening goal of the tie.
After linking up with Ozil in a deep position, Ramsey continued his run into the box and converted with a first-time finish across Alex Meret after Maitland-Niles knocked Lacazette's pass into the Welshman's path.
Napoli struggled to respond and they were soon two goals behind as Torreira turned Fabian Ruiz on the edge of the box and found the back of the net with his left-footed shot, albeit with a huge helping hand thanks to a deflection off Koulibaly's leg.
Sead Kolasinac's tame effort was then kept out by Meret, who was also equal to a couple of attempts from Aubameyang before the first half ended.
Arsenal could easily have taken a three-goal lead into the interval, with Lacazette fluffing his lines 12 yards from goal and Ramsey having another shot dealt with.
Napoli created just one goalscoring opportunity in the opening 45 minutes and it came shortly before the referee blew his whistle, but Lorenzo Insigne could not keep his shot down when perfectly picked out by Jose Callejon in front of goal.
Carlo Ancelotti's side were a lot more like their usual selves early in the second period, coming close to a goal 54 minutes in through Koulibaly's header, which Petr Cech - at fault for giving away the corner - was able to tip over the bar.
Arsenal had another couple of opportunities to all but kill off the tie, with Ramsey's powerful shot being slapped to safety and Nacho Monreal guiding the subsequent corner over the bar after being left unmarked.
Both teams continued to enjoy threatening moments as the game entered the final 20 minutes.
Napoli were indebted to Meret for producing a double save to frustrate Kolasinac and Maitland-Niles, while up the other end Piotr Zielinski diverted Insigne's cross over the crossbar with plenty of the goal to aim for.
Despite the positive of a clean sheet, Emery will perhaps be disappointed that his side did not further strengthen their lead as Ramsey missed from 10 yards late on and Aubameyang was also off target from a similar position.
The two sides will meet again in the return leg at the Stadio San Paolo in a week's time.
ARSENAL (3-4-1-2): Cech; Sokratis, Koscielny, Monreal; Maitland-Niles, Torreira (Elneny 77'), Ramsey, Kolasinac; Ozil (Mkhitaryan 67'); Lacazette (Iwobi 67'), Aubameyang
NAPOLI (4-4-2): Meret; Hysaj, Maksimovic, Koulibaly, Rui; Callejon, Allan, Ruiz (Ounas 82'), Zielinski; Mertens (Milik 66'), Insigne (Younes 82')