Italy defender Chiellini opened the scoring 10 minutes into his first start since suffering a calf injury in December, only to see it cancelled out by Gokhan Inler's deflected long-range strike two minutes from half-time.
The draw means champions Juve move up to 59 points with 11 games left while Napoli have now drawn four games in a row.
Chiellini sparked the incident, in a high-pressure game where Napoli fans had pelted the Juve team bus with stones before kick-off, by pulling the Uruguayan's hair.
"I think we shown how much we want to win the league this year," Chiellini told Sky Sports Italia.
"We're happy with our performance and it's a shame that we didn't win as we hoped to, but it was the right result.
"It [my calf] still hurts. I have to thank the medical staff. We've worked into the night every day and even at home. "I'm happy to have helped the team today, even if I know that I have to improve physically."
"You can see what happened from the video, but at the end of the day it's right that we have a good go at each other and the referee decides. After the match it's all over," Chiellini added.
"Giorgio was looking to see what kind of gel Cavani was wearing," he joked.
"It was a test of character and despite the fiery atmosphere we kept our cool and we were always in the game.
We're six points ahead... but there are still 11 games left in which we have to go to Inter and Lazio and have Milan at home and next week we have to take on this season's revelation, which is Catania. Every match can bring surprises."
Walter Mazzarri's side reacted well to going behind and pushed Juve back but struggled to create clear-cut chances against a defence well-marshalled by Chiellini.
Juve paid for their wastefulness when Inler's effort was deflected by Leonardo Bonucci's head over Gianluigi Buffon And into the net.
