Ramsey finished off a stunning move to open the scoring and Lucas Torreira's drive deflected in off Koulibaly to double Arsenal's advantage before the break at Emirates Stadium on Thursday.
Serie A side Napoli struggled to impose themselves on the contest, although Lorenzo Insigne and Piotr Zielinski had big opportunities, and Carlo Ancelotti's men have work to do in next week's return.
Koulibaly made a superb pair of blocks to repel Ramsey and Ainsley Maitland-Niles but he could do nothing about Arsenal's excellent opener in the 14th minute.
Ramsey's interception sparked a tremendous team move, the midfielder swapping passes with Mesut Ozil before Alexandre Lacazette and Maitland-Niles combined beautifully to set up the Wales international for a placed first-time finish.
Arsenal scored a second in the 25th minute, Torreira turning into space outside the Napoli box and seeing his drive take a decisive deflection off Koulibaly.
The Gunners continued to pile forward but, after Lacazette miscued and Pierre-Emerick Aubameyang tested Alex Meret, Insigne missed a great chance before the break.
Napoli improved after the interval with the offside flag ruling out an Insigne goal and Koulibaly forcing a fine save from Petr Cech with a powerful header.
Arsenal pushed for a third, though, with Meret superbly keeping out Ramsey's drive and Nacho Monreal planting a free header over the crossbar from the resulting corner.
The impressive Meret made a double save to deny Sead Kolasinac and Maitland-Niles and Zielinski missed a huge opportunity to score a crucial away goal for Napoli.
And Ramsey and Aubameyang should have made the visitors pay, wasting late chances to leave Napoli with some hope.
8 - Since the start of last season, Aaron Ramsey has been directly involved in eight goals in the Europa League (6 goals, 2 assists), more than any other Arsenal player. Swansong. #ARSNAP #UEL pic.twitter.com/EuiZkpnUQi— OptaJoe (@OptaJoe) April 11, 2019
What does it mean? Advantage Arsenal, but work to do
Arsenal's dreadful away form means they can take nothing for granted ahead of their trip to Naples. Unai Emery's side have won just twice away from home since November and those victories came against Huddersfield Town in the Premier League and Blackpool in the FA Cup. Napoli will surely be much better than in their limp London display, too.
Ozil makes Arsenal tick
The enigmatic Ozil was at his bewitching best in the first half, producing an individual performance at odds with his ineffective showing in a Premier League defeat at Everton last time out, during which he petulantly hurled his coat out of the dugout after being substituted. Ozil faded after the break but it was still a surprise to see him again withdrawn by Emery midway through the second period.
Insigne miss could be costly
Napoli's attackers were starved of service for the most part, but when a big chance came the way of Insigne on the stroke of half-time he missed the mark. Jose Callejon found Insigne in a fantastic position but his effort soared over Cech's goal. An away goal could have been key and the second half would have been a different prospect at 2-1.
Key Opta Facts
- Arsenal have been beaten just once in their last 18 home games in the UEFA Cup/Europa League (W13 D4).
- Napoli have never beaten an English side away from home in European competition (P9 W0 D1 L8).
- Arsenal scored with their first two shots on target of the game.
- Napoli had just two shots on target, their lowest total in a game in any competition this season.
- Since the start of last season, Aaron Ramsey has been directly involved in eight goals in the Europa League (6 goals, 2 assists), more than any other Arsenal player.