Carlos Tevez created Juve's opener, turning De Rossi before playing in Arturo Vidal to fire past Morgan de Sanctis.
Immediately after halftime, Juve doubled the lead as Andrea Pirlo's free-kick found an unmarked Leonardo Bonucci, who forced in the home team's second for the night.
De Rossi was then shown a straight red card for an ugly challenge on Giorgio Chiellini and minutes later he was followed by Castan.
The defender was sent off for using his hand in a goalline clearance on Chiellini's header. It was inevitably also a penalty and substitute Mirko Vucinic converted against his former club.
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