Maybe it's because they don't want to lose against their former manager that's why they put in a hell of a performance. They totally dominated the game in every aspect with the exception of possession. This win gives the likes of Inter Milan and Lazio belief that they can do something before the season is entirely over.
It could be their reason because there is Sarri in the Juventus camp. But I hope that Naples is really in the process of getting better. Because if they only play because they want to show someone then this is dangerous for their journey in the final standings later. They might not enter the European zone though