Carlos Tevez and Gonzalo Higuain scored two apiece to take the clash to spot kicks, where Simone Padoin missed the crucial effort to hand the trophy to the Partenopei.
Rafael saved Giorgio Chiellini and Simone Padoin's efforts from 12 yards at the Jassim Bin Hamad Stadium in Doha to give Napoli its first win in the competition since 1990 and deny Massimiliano Allegri his maiden piece of silverware at Juve.
Two Argentina internationals had battled for the headlines before that, with Carlos Tevez netting twice for the Serie A champions and Gonzalo Higuain responding with a double for the Coppa Italia winners.
A defensive mistake gifted Tevez the opening goal of the game – his 14th of the season in all competitions – after five minutes, the striker taking full advantage with a composed finish.
Higuain leveled things up seven minutes after the hour, Tevez's compatriot heading home his first goal in seven games.
That forced extra time, where Tevez looked to have secured a seventh Supercoppa Italiana crown for Juve early in the second period, but Higuain had other ideas with a last-gasp strike to force penalties.
In the shooutout, Tevez missed Juve's first kick, but it was Padoin's failure that gave Napoli victory - Rafael diving to his right to palm the ball away despite some earlier heroics from Gianluigi Buffon.
The two sides now begin their midseason break, but will face each other again in their second games back in January at San Paolo.
Napoli made a shocking start to the match as some calamitous defending handed Tevez the breakthrough.
Raul Albiol and Kalidou Koulibaly challenged each other for a header 20 yards from goal, the loose ball dropped to Tevez and he advanced before coolly slotting under Rafael.
Napoli refused to let such a soft goal get to them and, after Jose Callejon had blazed over, Marek Hamsik was denied by the post.
The Napoli captain brought the ball down well and unleashed a low shot that deflected off Giorgio Chiellini but, with Gianluigi Buffon beaten, struck the upright.
Callejon should have brought his side level after 54 minutes following a pinpoint pass from Hamsik, the Spaniard controlling the ball perfectly only to drag his effort agonisingly wide.
Napoli continued to enjoy the better of things and deservedly drew level after 67 minutes as Higuain guided home De Guzman's left-wing cross.
Neither side was able to find a winning goal inside the 90 minutes, but Tevez appeared to have earned the win in the 106th minute, collecting a pass from Paul Pogba and firing into the bottom corner.
However, Higuain took the match to penalties with a poacher's finish, the 27-year-old reacting fastest to poke Dries Mertens' blocked shot beyond Buffon with two minutes remaining.
Both sides missed their opening efforts but Juve fluffed their lines three times with the scores at 5-5, with Padoin's miss proving decisive after Koulibaly had netted to make it 6-5.