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.
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