Emery's men took control of the tie with a dominant first-half performance at the Emirates Stadium.
Aaron Ramsey opened the scoring with a cool finish to cap a flowing move and the Gunners were further ahead before half-time when Napoli defender Kalidou Koulibaly deflected Lucas Torreira's shot into his own net.
Arsenal couldn't add to the lead after the break, but they had done enough to put themselves in pole position ahead of the second leg in Naples on April 18.
However, Emery is well aware that Arsenal have a wretched away record this season, while Napoli should be a more formidable force in front of their vociferous fans at the San Paolo Stadium.
Arsenal still control top-four race: Emery
"The first leg was very important to take a good result. We deserved to win, but we know it is going to be very difficult there," Emery said.
"Their performances at home are usually very strong. We will plan to win the match, but we need to have a lot of respect for them.
"It is still 50-50. Our challenge is to be competitive away. Sometimes away we lost the spirit we have at home."
Napoli boss Carlo Ancelotti remains confident of a second-leg comeback.
"The first half we were really bad. We weren't brave enough to control the game as we wanted," he said.
"The result is difficult to change but we have 90 minutes left. In the second half we showed we create chances.
"It will be a different environment with our home crowd behind us. I'm confident."
It was a much-needed success for Emery, who this week called on his players to embrace the pressure of regaining their Champions League status after two successive seasons out of Europe's elite club competition.
With Arsenal sitting fifth in the Premier League after Sunday's damaging defeat at Everton, the Gunners can no longer rely on their domestic fortunes to qualify for the Champions League.
Winning the Europa League is Arsenal's other route back into the Champions League.
Having won the Europa League three times during his tenure as Sevilla boss, Emery knows the value of a first-leg lead and he sent out an attacking line-up featuring Pierre-Emerick Aubameyang, Alexandre Lacazette and Mesut Ozil.
Arsenal up to third as Ramsey, Lacazette sink Newcastle
A fired-up Arsenal needed just 15 minutes to take the lead.
A stylish move carved Napoli open as Ramsey and Ozil exchange passes in midfield before Lacazette fed Ainsley Maitland-Niles.
Ramsey had continued his run into the Napoli area and the Wales midfielder met Maitland-Niles' pass with a composed close-range finish for his sixth goal of the season.
It was the perfect way for Ramsey to announce himself to an Italian audience ahead of his close-season move to Juventus.
Torreira is one of the midfielders who will take over from Ramsey and the Uruguayan showed why that should be a smooth transition as he helped double Arsenal's advantage in the 25th minute.
Tigerishly dispossessing Fabian Ruiz inside the Napoli half, Torreira accelerated towards the penalty area, cleverly checked back to open up more space and drilled a low shot that took a hefty deflection off Koulibaly as it looped into the net.
Without a win in seven visits to England, Napoli's hopes of ending that barren run dwindled even further when Lorenzo Insigne blazed over from close range.
Napoli tried to rally after the interval, but Koulibaly's header was tipped over by Petr Cech, while Piotr Zielinski blew their best chance when he missed the target with only the keeper to beat.
Arsenal remained dangerous and it took a good save from Alex Meret to deny Ramsey before Maitland-Niles was also frustrated by the over-worked Napoli keeper.
Ramsey should have put the result beyond doubt when he shot over in the closing stages, but Arsenal will still travel to Italy in confident mood next week.
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