Napoli were ahead with the first real chance of the game as Edinson Cavani buried a superb assist from Marek Hamsik.
Hamsik himself could have doubled the score after 18 minutes but he could not find the target.
Blerim Dzemaili had a similar chance to double the advantage 15 minutes later, but he shot wide when well placed.
In the second half Napoli continued to press and Goran Pandev headed wide in the 59th minute.
Alessio Cerci had a good chance to equalise with 10 minutes remaining but couldn't find the target with his shot.
Napoli were made to pay for their profligacy as Gianluca Sansone scored late on to steal a point for Torino.