Miralem Pjanic converted the 28th-minute free-kick after Napoli's young goalkeeper Alex Meret was sent off for a professional foul on Cristiano Ronaldo and Emre Can made it 2-0 before half-time.
Despite operating with reduced numbers, Napoli hit the post through Piotr Zielinski between the Juve goals and Pjanic's second yellow card for deliberate handball gave them hope – as did Jose Callejon's 61st-minute goal.
Insigne provided a superb assist but could not complete the comeback after Alex Sandro fell foul of a VAR review for handball having blocked Fabian Ruiz's goalbound shot.
Napoli's relentless pressure then dropped off and Massimiliano Allegri's undefeated Juve now boast a mammoth 16-point lead over Carlo Ancelotti's men at the summit.
Zielinski arrowed a first-time shot just wide in the 11th minute following an error by Juventus centre-back Leonardo Bonucci.
Ronaldo thrashed his first opening over but was in the thick of the game's first turning point, when Meret dashed from his area to rashly bring down the Juve superstar after Kevin Malcuit's dreadful backpass sold him short.
Ancelotti sacrificed Arkadiusz Milik to bring on David Ospina and the substitute goalkeeper's first act was to pick Pjanic's immaculate free-kick out of his net.
Napoli thrillingly took the game to Juve despite reduced numbers, with the irrepressible Zielinski thudding a shot against the post.
Ospina beat another sweet Pjanic strike over the bar in the 39th minute, only for Can's deflected header from a well-worked short corner to double the advantage.
Pjanic had been booked for a 36th-minute foul on Callejon and the game took another twist when he walked early in the second half.
And Callejon breathed new life into Napoli's challenge as he turned in Insigne's brilliant left-wing cross from close range.
Wojciech Szczesny saved on the angle from Zielinski amid blue waves of attacks before his post denied a crestfallen Insigne from 12 yards.
Juve ride out the storm, sailing closer to invincibility
Further notable challenges await Allegri's team in Serie A this season, with games against both Milan clubs and a derby showdown versus Torino among them. But coming through this wild, wonderful encounter intact feels like a significant step towards an unbeaten season.
Zielinski dazzles in vain
Whether this game was 11 versus 11, 10 versus 11 or 10-a-side, Napoli's Poland midfield star was a relentless problem for Juve. He tested the post and threatened persistently from the left flank before being moved inside after half-time, where his influence did not diminish.
