The reigning champions won thanks to goals from Alisson Santos after seven minutes and a 68th-minute strike from Eljif Elmas before Cesare Casadei scored a late consolation for Torino.
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Napoli move to within a point of second-placed AC Milan, who need to beat leaders Inter in the Milan derby on Sunday to have any chance of staying in the title hunt.
To add to Napoli’s positive night, Kevin De Bruyne came on as a second-half substitute for his first appearance since tearing his hamstring in October.