An own goal by Christian Maggio and a calm finish by Mirko Vucinic in the first half of extra time gave Juventus the first trophy of the season after Napoli had twice led in normal time at a rain-soaked Bird's Nest.
Italian Cup winners Napoli lost goal-scorer Goran Pandev and Juan Camilo Zuniga in the last 10 minutes of normal time through red cards, while coach Walter Mazzarri was also sent off, for dissent.
Pandev was shown a straight red for abusing a linesman, and Zuniga was dismissed for two bookable offences.
Juventus' new signing Kwadwo Asamoah showed his worth on his debut by scoring the first goal and setting up the fourth, and he continually troubled Napoli down the left wing.
Juventus, who went unbeaten last season, were dealt a blow on Friday when coach Antonio Conte was banned for 10 months over a match-fixing scandal, but the Turin club showed no signs of pressure as they took early control.
Napoli took the lead against the run of play in the 27th minute through Edinson Cavani. Juventus keeper Gianluigi Buffon came off his line to make a valiant save but the striker slotted in the rebound.
Juventus equalised through Asamoah 10 minutes later, when the Ghana midfielder found the net with a powerful left-foot shot from outside the box.
Napoli restored the lead three minutes later after another defensive lapse from Juventus. Leonardo Bonucci's attempted clearance hit Pandev, who calmly flicked the ball over an advancing Buffon.
Juventus equalised for the second time when Arturo Vidal converted a penalty in the 74th minute after Vucinic was brought down.
