Arkadiusz Milik scored the winning spot-kick after Paulo Dybala had seen his first for Juve saved, before team-mate Danilo blazed the second over.
This followed a hard-fought 0-0 over 90 minutes of few chances, played behind closed doors at the Stadio Olimpico.
It gives Napoli boss Gennaro Gattuso his first major trophy as a manager.
However, for his opposite number Maurizio Sarri it is another lost piece of potential silverware.
So far in his career – which included a transformational three-year spell at Napoli that saw them regularly challenge for the title – Sarri has just last season’s Europa League to his name, from his one campaign with Chelsea.
With the Coppa Italia semi-final second legs and final serving as a precursor to the return of the Italian top-flight, it was clear over 90 minutes that neither side is yet fully up to speed.
There was little to truly get excited about, although Napoli’s Lorenzo Insigne did strike the post with a superb free-kick before Juve’s legendary 42-year-old goalkeeper Gianluigi Buffon was forced into a smart save to deny Diego Demme from close range.
Arguably the best moment of normal time came with just seconds remaining, as Buffon was forced into another decent save to parry a Nikola Maksimovic header from a corner before Eljif Elmas somehow conspired to fire his follow-up against the post.
That took us to the shootout, which Juve handed to Napoli courtesy of two initial failures.
The first spot-kick from Dybala was at a perfect height for Alex Meret to push away, while the second was woefully dispatched over the bar by Danilo.
With Insigne, Matteo Politano and Maksimovic all scoring, it left Milik to seal the success, which he did with a coolly-taken effort into the bottom corner.