Napoli had the luxury of choosing from a near full strength squad, while Chiellini was passed fit to start for Juventus. The captain had been in doubt after suffering from a bruised ankle.
The hosts tested the Juventus backline with two early Marek Hamsik efforts, before the visitors took the lead on ten minutes. Pirlo's cross from the left was headed in by Chiellini, who rose above Miguel Britos to net his first goal of the season.
Stephan Lichtsteiner went down under minimal contact from Inler in the box and was livid not to get a penalty. Hamsik and Edinson Cavani then linked up to provide Goran Pandev with a chance, but the Macedonian was crowded out by Andrea Barzagli in the area.
Juventus should have doubled their advantage on 18 minutes. A long Gianluigi Buffon clearance was picked up by Sebastian Giovinco. The Atomic Ant squared the ball for Mirko Vucinic, only for Morgan De Sanctis to deny a certain goal with an outstretched palm wide.
A nasty clash of heads between Britos and Inler caused a short delay with Britos suffering a second knock when his head hit the turf. The defender looked out of sorts when he got back up, but remarkably opted to carry on playing.
A poor touch from Vucinic scuppered another Juventus chance after Giovinco threaded through. Juventus were made to pay from their wastefulness when Napoli equalised with a slice of fortune two minutes before the break.
Inler unleashed a screamer from distance which bounced off Leonardo Bonucci's head and over a diving Buffon into the top corner. It was Napoli's first goal in over six and a half hours of Football. Arturo Vidal picked up a costly booking which rules him out of next weekend's game with Catania.
Cavani threw a careless elbow into Chiellini's face in first half stoppage time. The referee missed it, but the third official didn't. After deliberating the decision, the striker was only given a caution and in truth was lucky to stay on the field. He led with intent.
To no-one's surprise, Britos was withdrawn during the break as a precautionary method. Juventus started the second period the brighter of the two sides. Lichtsteiner dispossessed Juan Zuniga and played in Giovinco, whose right wing cross just evaded Vucinic.
Hamsik stung Buffon's palms from distance with Napoli's first effort of the second half just before the hour mark. Inler called Buffon into action again with a low effort, while at the other end Federico Peluso fired over the bar.
Inler saw a strike cannon off two defenders in the box, as loud handball appeals fell on deaf ears. Bonucci headed another set piece off the line and a Lichtsteiner tug on Pandev in the six yard box went unpunished.
At the halfway point, Vucinic fizzed a shot which almost caught a flailing De Sanctis unaware. No Juventus player was able to latch onto the follow up and the danger was cleared. Christian Maggio managed to shake off Peluso, only to see his near-post strike thwarted by Buffon.
Cavani had been well marshalled by the Juventus defence, but on 73 minutes he managed to get in front of Bonucci, only to send his header too close to Buffon. Napoli really should have taken the lead a minute later. Buffon punched a Hamsik drive back into the danger zone, Blerim Dzemaili reacted instantly, but not accurately and the ball finished the wrong side of the post.
Antonio Conte brought Alessandro Matri into the game as he made his first change. Hugo Campagnaro intercepted a dangerous Lichtsteiner cross, before a wild Matri half-volley ended up in the crowd. In his final contribution, Inler tried to replicate his first half goal, but Buffon was equal to the effort and tipped the ball over.
With three minutes remaining, Peluso brought Cavani down on the edge of the box. El Matador wasted the chance to be the partenopei's saviour by curling his effort over the bar.
Napoli: De Sanctis; Cannavaro, Campagnaro, Britos; (Dzemaili 46) Maggio, Inler, (Armero 84) Behrami, Zuniga; Hamsik, Pandev; (Insigne 67) Cavani
Juventus: Buffon; Barzagli, Bonucci, Chiellini; Lichtsteiner, Pirlo, Vidal, Marchisio, (Padoin 90) Peluso; Giovinco, (Matri 74) Vucinic (Pogba 85)
Goals: Chiellini 10 (J) Inler 43 (N)