Skipper Lorenzo Insigne scored a brace for Napoli including the 67th-minute winner and had a role in Dries Mertens and Jose Callejon’s goals for the southerners.
In Parma, Chiellini made the difference early, connecting with an Alex Sandro deflected shot to fire in from close range after 21 minutes in Emilia Romagna.
“He (Sarri) can be proud because the team have shown that we are united, that we can train with dedication and application. We will improve, but the important thing is to grow by winning,” said 35-year-old Chiellini after just his 27th goal in his 14-year Juventus career.
Sarri’s arrival has been hailed as the dawn of a new era for Juventus with a different exciting style of football.
But the Turin giants new-look side mirrored Massimiliano Allegri’s of last season.
Apart from Argentine Gonzalo Higuain, back from a loan to Chelsea, preferred up front alongside Cristiano Ronaldo in place of Paulo Dybala, the team was the same as last season.
New Dutch defender Matthijs De Ligt remained on the bench with Welsh international Aaron Ramsey not in the group, while French midfielder Adrien Rabiot came on after an hour in place of Sami Khedira.
“I spoke to him before, during the break and at the end of the game, when obviously he was much happier with the result,” he said.
“Being a perfectionist he was still angry at the mistakes made.”
Martusciello defended the lineup, insisting “taking a gamble in the first game of the season would have been unnecessary”.
“This is a team full of champions.”
Ronaldo drew a blank with a goal ruled offside and several missed efforts against Parma who finished 14th on their return to Serie A last season.
Ronaldo squandered a golden chance after half an hour, controlling a Higuain cross with his chest but sending wide across the face of goal.
The Portuguese looked to have made up for his earlier error on 34 minutes, finishing off a Douglas Costa effort into the back of the net.
The goal was ruled offside after consultation with VAR with Ronaldo deemed to be marginally offside.
The five-time Ballon d’Or winner again proved wasteful after an hour latching on to a Costa cross but sending the ball over the top of goal.
His frustration continued five minutes later with Parma goalkeeper Luigi Sepe denying the Portuguese at full stretch.
“Great to start the season with three points!” the 34-year-old Ronaldo tweeted after the game.
In Florence, midfielder Erick Pulgar converted a penalty after just nine minutes to the delight of the home crowd and new club owner Italian-American media magnate Rocco Commisso.
But Mertens pulled Napoli back after 38 minutes with Insigne adding a second from the spot just before the break.
Nikola Milenkovic’s powerful header six minutes after the break kept Fiorentina, 16th last season, in the game.
Insigne set up Callejon for Napoli‘s third on 56 minutes and completed his own brace nine minutes later after substitute Kevin-Prince Boateng volleyed in a third for the hosts.
French midfielder Franck Ribery made his Serie A debut coming on the final quarter of an hour for Fiorentina and having a penalty appeal turned down.
“Juve are moving from one coach to the next, but we’ll try to play a great game with enthusiasm and focus, even if our most difficult match comes so early in the season.”