Edinson Cavani broke the deadlock with a penalty just after the hour and Marek Hamsik finished off a counter-attack as Napoli claimed their first trophy since the Maradona-inspired team won Serie A in 1989/90.
Juventus had substitute Fabio Quagliarella sent off in the 89th minute for a full-blooded elbow in the face of Salvatore Aronica after only 17 minutes on the pitch.
"This was a club that didn't exist, said Napoli president Aurelio De Laurentiis, a film-maker who refounded the club after it was declared bankrupt in 2004 and led it from Serie C back to the top flight.
"In a few years we've brought something home, above all the knowledge that Napoli exists, lives and can be the world champion of the sport."
Napoli coach Walter Mazzarri said: "It seemed unthinkable to beat Juve.
"They hadn't ever lost this season [in Serie A] and to beat them 2-0 was magnificent work. The team has done something extraordinary in the last three years: Cavani, [Ezequiel] Lavezzi, Hamsik are on everyone's lips, but it's an entire team that should be acclaimed as one."
"This was the 51st game of the season. Anyone who plays football knows that playing these games at that level is hard. We have paid in the championship for this. You can lose to anyone in our league, and we dropped too many points."
Although Juventus had completed their 38-match campaign in Serie A without losing, there was some debate over their 2-2 Italian Cup draw after extra time against AC Milan in their semi-final second leg.
Milan claimed that, as they were winning 2-1 at the end of 90 minutes, that should count as a Juventus defeat.
Del Piero, 37, was told earlier this season that his contract at Juventus would not be renewed and the talismanic forward was given a standing ovation when he was substituted midway through the second half.
Juventus coach Antonio Conte kept to his regular cup line-up with Marco Storari in goal instead of Gianluigi Buffon and a starting role for Del Piero, who has been used mainly as a substitute in Serie A.
Napoli, who finished fifth in Serie A and missed out on the Champions League by three points, were quickly on the attack as Hugo Campagnaro burst down the right and crossed for Juan Camilo Zuniga whose header was turned away by Marco Storari.
Lavezzi shot wide on the counter-attack while a fierce effort from Zuniga was charged down by Leonardo Bonucci.
Juventus had a penalty appeal turned down just before half-time when Claudio Marchisio claimed to have been felled by Aronica.
Napoli continued to push forward after the break and won a penalty when Lavezzi was upended by Storari and Uruguay forward Cavani sent the Juve goalkeeper the wrong way from the penalty spot.
Juventus, who had devoted much of their energy to protesting refereeing decisions, suddenly started playing and enjoyed their best spell of the match, forcing Morgan De Sanctis to make two excell
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