The Bianconeri, who started the game four points behind Gli Azzurri, took the lead with their first meaningful attack of the game after Paulo Dybala was able to slide a pinpoint ball into the feet of his fellow countryman Higuain, and the former Napoli man managed to beat Pepe Reina from the edge of the box.
Napoli, who were looking to protect an unbeaten run in Serie A, almost got back on level terms after 18 minutes when Marek Hamsik's fierce drive was punched away by Gianluigi Buffon.
The Neapolitans continued to press for a goal after the break when Dries Mertens played Lorenzo Insigne into a shooting position only for his effort to be comfortably gathered by Buffon.
Napoli thought that they had a case for a penalty with a quarter of the game left to play after Mertens fell to the ground under pressure from Chiellini, but his appeals were waved away.
In the end, Juve snuffed out any late hopes of a Napoli revival to end their opponents' unbeaten domestic run and close the gap at the top of Serie A.