Napoli went top of Serie A on goal difference following a 3-0 home success over Bologna on Sunday.
Last season's runners-up signalled their intent for the new campaign with an impressive display the Stadio San Paolo.
Marek Hamsik scored twice for the hosts, either side of half-time, after Jose Callejon had put Rafael Benitez's side ahead.
Inter had briefly gone top after defeating Genoa 2-0 at San Siro earlier in the day.
Goals in the final 15 minutes from Yuto Nagatomo and Rodrigo Palacio sealed the points for Walter Mazzarri's side.
Torino matched that result at home to newly promoted Sassuolo, with goals either side of the break from Matteo Brighi and Alessio Cerci proving the difference.
Roma also ran out 2-0 winners as two goals in as many minutes midway through the second half from Daniele De Rossi and Alessandro Florenzi handed them victory away at Livorno.
Their city rivals Lazio were 2-1 winners at home to Udinese.
Hernanes opened the scoring for the hosts after 13 minutes and Antonio Candreva doubled that advantage from the spot three minutes later.
Substitute Luis Muriel's goal on the hour was not enough for Udinese to claim anything from the game.
Cagliari had to come from behind at home to Atalanta to get off the mark with a 2-1 victory.
Guglielmo Stendardo struck first for the visitors after 27 minutes but that lead was cancelled out within a minute by Radja Nainggolan.
Matias Cabrera hit the winner after 63 minutes to hand all three points to Cagliari.
Elsewhere, Parma and Cheivo played out a goalless draw.