Napoli thrashed Bologna 3-0 on Sunday in Rafael Benitez's first league game in charge of the Partenopei to go top of Italy's Serie A on goal difference.
Champions Juventus had kickstarted the new season with a 1-0 away win at Sampdoria on Saturday while AC Milan, who finished third last season, were stunned 2-1 by a Luca Toni brace away at promoted Verona.
However a first-half opener from Jose Callejon and a brace from Slovakian forward Marek Hamsik sealed the points for Napoli, who lead the fledgling championship ahead of Inter Milan and Roma.
Napoli underwent major changes in the close season with last season's top scorer, Uruguayan Edinson Cavani, moving to Paris Saint-Germain and coach Walter Mazzarri leaving for Inter.
Former Real Madrid forward Gonzalo Higuain, brought in by Benitez as a direct replacement, made his league debut at the San Paolo but failed to hit the net as Hamsik stole the show with a scintillating performance.
Benitez, who only three months ago coached Chelsea to Europa League glory, said: "This is not an answer to Juve. We have our own gamplan as well," said the Spaniard.
"The team played well, but there's always room for improvement."
Earlier on Sunday Inter, whose 2012/13 campaign ended in a catastrophic ninth place finish, got off to a winning start with second half goals from Japan's Yuto Nagatomo and Rodrigo Palacio securing a deserved 2-0 win over Genoa to get Mazzarri's reign as coach off to a positive start.
Prior to this game, Inter had won only once in their last eight games, and Mazzarri said: "The boys hadn't won at home for several months and suffered a lot of defeats, so this win has helped exorcise the demons."
Elsewhere, Cup holders Lazio, thrashed 4-0 by Juventus in the Italian Super Cup last week, made amends with a 2-1 home win over Udinese.
Hernanes opened the scoring for Vladimir Petkovic's side in the 13th minute, with Antonio Candreva adding Lazio's second from the penalty spot three minutes later.
Udinese reduced the arrears on the hour thanks to substitute Luis Muriel and the northerners, who finished fifth last term to secure a Europa League spot, pushed their hosts all the way before conceding defeat.
French coach Rudi Garcia's first game in charge of Roma, an away trip to promoted Livorno, was a tense affair until Daniele De Rossi broke the deadlock in the 65th minute.
Alessandro Florenzi allayed fears further when he struck Roma's second only two minutes later to leave Roma, one of only three victorious teams not to concede a goal at the weekend, in third place.
Despite his joy at the win, Garcia was surprised when told he would be fined for using a telephone on the touchline.
"Fined? Really? In France it's not like this," he told Sky Sport Italia after being informed of his infringement.
"I used the phone because my radio wasn't working. I had to call my technical assistant who was watching the match up in the stands."
Torino hosted newly promoted Sassuolo in rain-hit Turin, where Matteo Brighi broke the deadlock in the 40th minute for the hosts and Alessio Cerci scored an unanswered second on the hour mark.
Cagliari also took all three points, but were down to a 27th minute opener from Atalanta's Guglielmo Stendardo before levelling a minute later through Radja Nainggolan, with Matias Cabrera scoring their second after finishing off a fine move in the 63rd minute.
It leaves Milan as the only major side not to claim all three points on the opening weekend of the campaign.
Milan had opened the scoring inside the opening quarter of an hour when midfielder Andrea Poli finished off a smart pass from Italy striker Mario Balotelli.
But the visitors were pegged back by Luca Toni on the half hour and left stunned when the former Fiorentina striker scored with his second header eight minutes after the restart.