Arkadiusz Milik scored the triumphant spot-kick after Paulo Dybala had seen his first for Juve spared, before partner Danilo blasted the second finished.
This followed a hard-battled 0-0 more than an hour and a half of not many possibilities, played in secret at the Stadio Olimpico.
It gives Napoli supervisor Gennaro Gattuso his first significant trophy as an administrator.
In any case, for his contrary number Maurizio Sarri it is another lost bit of possible flatware.
So far in his vocation – which incorporated a transformational three-year spell at Napoli that saw them normally challenge for the title – Sarri has recently last season’s Europa League to his name, from his one battle with Chelsea.
And keeping in mind that his side at present top Serie A, they are a long way from guaranteed of making sure about a ninth consecutive title and his first trophy on home soil, with their lead over second-set Lazio only one point.