Juve had won its past three top-flight games by the same 2-0 scoreline but its title prospects took another dent with defeat to a spirited Napoli side at Estadio Diego Armando Maradona.
Giorgio Chiellini marked his landmark 400th Serie A appearance by giving away a penalty that was put away by Insigne for what proved to be the only goal of the contest.
Cristiano Ronaldo and Alvaro Morata went close to equalising but the visitors, who beat Napoli 2-0 in last month's Supercoppa Italiana, could not find a way through.
Napoli was already without a number of key men and lost first-choice goalkeeper David Ospina to injury in the warm-up, meaning a late call-up to the side for Alex Meret.
The hosts were fortunate to see Federico Bernardeschi balloon a promising chance into the stands but took the lead 31 minutes in through Insigne's powerful penalty.
Chiellini jumped with his arm and caught Amir Rrahmani in the face, which VAR adjudged was worthy of a spot-kick, and Insigne did not waste the chance to bring up his century.
Juve, which had not conceded in its previous three Serie A games, should have been level early in the second half but Ronaldo fired straight at Meret from close range.
Meret was also equal to Federico Chiesa's drive and Morata had a goal ruled out after another Chiellini foul on Rrahmani in the build-up as Juve continued to press.
A final chance fell Morata's way late on but he could not get the better of inspired Napoli keeper Meret, who produced a fine save with his legs to help his side to a huge win.