The Italian champions picked up where they left off at the end of last season's triumphant campaign – with Victor Osimhen banging in the goals and Napoli winning.
Matteo Politano got Napoli's first goal of the season, cancelling out Frosinone's early advantage from Abdou Harroui's spot kick.
Last season's Serie A top scorer then helped himself to a superbly taken brace as the Azzurri ran out 3-1 winners.
Rudi Garcia's side will be reunited with their fans at the Stadio Maradona next weekend with Sassuolo providing the opposition.
Frosinone 1-3 Napoli (HT 1-2)
Scorers: Harroui 7 (pen), Politano 24, Osimhen 42, 79.
FROSINONE: Turati; Oyono, Monterisi, S. Romagnoli, Marchizza, Harroui, Mazzitelli (Brescianini 75), Gelli, Baez (Canotto 75), Cuni (Borrelli 67), Caso (Kvernadze 67).
Coach: Di Francesco.
NAPOLI: Meret; Di Lorenzo, Rrahmani, Juan Jesus, Olivera (Mario Rui 76), Cajuste (Anguissa 46), Lobotka (Ostigard 90+1), Zielinski, Politano (Elmas 76), Osimhen, Raspadori (Simeone 81).
Referee: Marcenaro (Genoa).
Booked: Oyono, Lobotka, Cajuste, Olivera, Mazzitelli.