To add insult to injury, Napoli had their own penalty appeal turned down immediately before Juventus were awarded their second.
Paulo Dybala converted both spot kicks for Juve and his fellow Argentine Gonzalo Higuain scored in between after Jose Callejon had given the visitors a halftime lead.
It was Higuain's second goal in as many meetings against Napoli since he left them to join Juventus in July after scoring a record 36 Serie A goals last season.
Higuain had two years to run on his contract with Napoli, who did not want to sell him, but moved after the Turin club agreed to pay a 90 million euro ($98.83 million) buyout clause in his contract.
"This evening, we suffered a defeat because of decisions which were not debatable, but were shameful and harmed the whole of Italian football," said Napoli director Cristiano Giuntoli.
Juventus coach Massimiliano Allegri, however, said that the two penalties awarded to his team appeared to be correct. "In any case, we can't reduce our performance to just the two penalty episodes," he said.
Poland forward Arkadiusz Milik made his first start for Napoli since suffering a knee ligament injury in October and was involved in the move which ended with Callejon turning the ball in from a narrow angle in the 36th minute.
Juventus levelled within a minute of the restart when Kalidou Koulibaly mis-timed a tackle on Dybala who converted the penalty himself.
Higuain then scored from the acutest of angles in the 64th minute when the ball fell to him after Pepe Reina completely missed Juan Cuadrado's cross.
Napoli had their own appeal turned down, claiming Raul Albiol had been tripped. Juventus immediately broke upfield before Reina dived at the feet of Cuadrado, who went tumbling over.
Replays showed that Reina got a hand to the ball before making contact with the Colombian but referee Paolo Valeri pointed to the spot and Dybala converted again.
"What am I supposed to do, disappear?" said Reina. "This evening, the result was decided by the refereeing decisions, the whole of Italy saw it."
(Writing by Brian Homewood in Berne; Editing by Toby Davis)
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