Napoli dispatched Bologna 3-0 at home on Sunday to go top of Serie A on goal difference.
Last season's runners-up staked their claim to the Scudetto with an impressive display at the Stadio San Paolo, where Marek Hamsik turned out to be the hero.
The Slovakia international, after Jose Callejon had put Rafael Benitez's side ahead in the 32nd minute, doubled their lead at the injury time of the first half. He then sealed the win with another goal in the 65th minute.
Inter, under the guidance of former Napoli manager Walter Mazzarri, also drew the first blood of the new season with a 2-0 win over Genoa at home.
Goals in the final 15 minutes from Yuto Nagatomo and Rodrigo Palacio put Inter beyond Genoa's chase.
Mazzarri said the win could help his side "exorcise the psychosis" of last season.
"These lads had not won at home for many months and suffered so many defeats here last year, so they needed this win to exorcise the psychosis," he said.
"I tried to reassure the squad, as I knew Genoa would sit and wait for us. I am happy for the lads, also for their first half performance. The substitutions were studied and planned, it all went the way we thought it would," he said.
Torino beat newly-promoted Sassuolo 2-0 at home, 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.
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