Napoli have scored nine goals in their opening three games, silencing critics who expected them to struggle after Juventus triggered a 90 million euro (£76.15 million) buyout clause in Higuain's contract to poach the Argentine from them.
Higuain, who scored a Serie A record 36 goals for Napoli last season as they finished runners-up, drove home a pass from Paulo Dybala then acrobatically volleyed home Sami Khedira's looping header from 12 metres.
Miralem Pjanic, signed from last season's third-place finishers AS Roma, added a third before the half hour to leave Juventus with nine points from three games. Luca Antei replied for Sassuolo.
Marek Hamsik gave Napoli the lead at Palermo shortly after halftime to overhaul Diego Maradona's total of 81 Serie A goals for the club before Jose Callejon added two more.
Roberto De Zerbi was making his debut as Palermo coach after Davide Ballardini resigned, suggesting another turbulent campaign for the Sicilians who employed seven coaches last season, two of them twice.
(Writing by Brian Homewood; Editing by Toby Davis)
