The match went into extra-time after Carlos Tevez’s fifth minute opener for Juve was cancelled out by Gonzalo Higuain midway through the second half.
Tevez scored again in the 106th minute but Higuain levelled the game at 2-2 12 minutes later to take the match to a penalty shootout.
Both sides missed their first spot-kicks, with Jorginho’s effort saved by Juventus keeper Gianluigi Buffon before Tevez struck the right post.
When Alvaro Morata levelled things up at 4-4 it went to sudden death, with Buffon saving Dries Mertens’ effort before Rafael kept out Giorgio Chiellini’s spot-kick.
The Juve goalkeeper made another save to deny Jose Callejon to give his side the advantage, but Roberto Pereyra sliced his penalty high above the bar. Kalidou Koulibaly then gave Napoli the edge, as he scored to put the shootout 6-5 in their favour.
The stage was then set for Rafael, who kept out Padoin’s effort to claim victory for Napoli.
The early momentum swung in Juve’s favour when a mix up between Koulibaly and Raul Albiol saw the latter nod the ball into Tevez’s path, who opened the scoring from close range.
Marek Hamsik almost equalised shortly after as Chiellini tried to knock down a high ball into the box, but it dropped kindly for the Napoli midfielder, who fired towards goal and luckily for Buffon, hit the post.
Juventus held on to their 1-0 lead until the break but Callejon went close when he put the ball wide from just a few yards out in the 55th minute before Higuain hit the post five minutes later.
Napoli were applying the pressure and it finally told in the 68th minute when Higuain lobbed Christian Maggio’s cross past Buffon.
No more goals were forthcoming in normal time, despite efforts from both sides, so extra-time was played, with Paul Pogba setting up Tevez for his second of the night in the second period.
The Argentina international slotted it past Rafael and Juve looked to have wrapped up victory until Higuain levelled again with two minutes left on the clock.
The late equaliser meant the match was to be decided on penalties, which Napoli won despite Buffon’s best efforts with three saves, as Rafael and the woodwork edged Napoli to a sudden death victory.