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The Cote d'Ivoire international had opened the scoring before Kevin Strootman later added a second to give the Giallorossi a comfortable 2-0 half-time lead.
However, an own goal from goalkeeper Morgan De Sanctis and Dries Mertens helped the Partenopei back into the contest, before the former Arsenal winger pounced in the closing stages to give Rudi Garcia's men the advantage ahead of the second leg.
Garcia's troops needed just 13 minutes to edge ahead in the clash, with Gervinho racing clear of the defence after a neat pass from Francesco Totti, before dinking over the out-rushing Pepe Reina to give his team the lead.
Strootman doubled the advantage shortly after the half-hour mark, advancing through heart of the midfield unmarked before producing a 25-yard screamer to stun the Partenopei and give Rafael Benitez's charges a mountain to climb in the second half.
The task was not beyond them, though, with the Naples-based outfit reducing the deficit within two minutes of the restart through their former goalkeeper De Sanctis.
Mertens completed the comeback on 70 minutes, skipping past a challenge before firing beyond De Sanctis, but Gervinho snatched victory for the capital club in the closing stages to render Napoli's spirited comeback academic.