Having secured a 2-0 victory in the first leg, the Gunners travelled to Naples knowing their fate was in their own hands.
Alexandre Lacazette's free-kick nine minutes before half-time secured a 1-0 victory and a 3-0 aggregate success to set up a semi-final clash with Valencia.
With plenty of question marks surrounding their away form, Arsenal have now won at Watford and Napoli in the space of three days to return to the Premier League top four and advance in Europe.
They fell at the semi-final stage to Atletico Madrid a year ago and LaLiga opposition again stand in their way of reaching the showpiece final.
This game may have lacked the drama of Tottenham's stunning Champions League win over Manchester City or the goalfest at Stamford Bridge as Chelsea saw off a spirited Slavia Prague comeback to reach their own Europa League semi-final, but Arsenal got the job done.
They were the better team across both legs and will now face Emery's former club Valencia for a place in this season's final in Baku on May 29, the Spaniard once again proving he is the master of this competition.
No manager has won more knockout games in the Europa League than the Arsenal head coach, who won three consecutive titles while at Sevilla.
Emery said Arsenal would go for it and he stuck to his word as both Lacazette and Pierre-Emerick Aubameyang started in attack, the visitors starting the game on the front-foot looking for a goal to all-but kill off the tie.
But, in committing men forward, they presented Napoli with the game's first decent chance as Aubameyang lost possession and the hosts broke, working the ball into Jose Callejon whose shot was well-saved by the legs of Petr Cech.
Arkadiusz Milik, recalled by Carlo Ancelotti having been on the bench for the first leg, finished well only to be denied by the offside flag before he headed wide when picked out in front of Cech's goal.
Arsenal suffered a blow as Aaron Ramsey, who opened the scoring at the Emirates Stadium last week, was forced off just after the half-hour mark with a hamstring problem.
But they would soon be celebrating as Lacazette dusted himself off having been fouled 30 yards from goal and curled a free-kick over the wall, badly wrong-footing Alex Meret in the Napoli goal to put Arsenal ahead on the night and in charge of the tie.
The lead should have been doubled soon after the break, Henrikh Mkhitaryan - on for the injured Ramsey - playing in Aubameyang, only for Meret to make a superb stop to deny the Gabon striker.
Napoli were kept at arm's length by a determined Arsenal side, showing much more guile and threat than they mustered in beating Watford's 10-men 1-0 on Monday night.
There was an occasional threat to Arsenal's lead but Cech's most difficult save came as a cross bounced off team-mate Nacho Monreal and had to be kept out.
For all the criticism often aimed at the Arsenal defence, they have now kept six clean sheets in their last seven games and managed to keep consecutive clean sheets away from home across all competitions for the first time since January 2017.
They will face Valencia at home on May 2 and will hope to head to the Mestalla with a similar lead which they travelled to Napoli with - all with the intention of going a step further than last season and reaching the final.
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