Edinson Cavani followed up Wednesday's hat-trick against Lazio by converting a second-half penalty on Sunday to give Napoli a 1-0 win at Sampdoria and end their opponents' unbeaten record in Serie A.
Fabrizio Miccoli scored a brilliant hat-trick, including an astonishing volley from around 40 metres, as Palermo hammered Chievo 4-1 to claim their first win of the season.
Torino scored four goals in a quarter-of-an-hour during the second half to win 5-1 at Atalanta, who hit the woodwork twice and took the lead as they dominated the first half, and Bologna thrashed Catania 4-0.
Cagliari, playing a home match in front of supporters for the first time this season, lost 2-1 to Pescara to remain winless.
Napoli's win kept them neck and neck with leaders and title-holders Juventus, who thrashed AS Roma 4-1 on Saturday.
The leading pair each have 16 points from six games, four more than Lazio and Inter who both won 2-1 at home.
Inter Milan enjoyed a fortuitous 2-1 win over 10-man Fiorentina.
Argentine striker Diego Milito fired Inter ahead from a penalty harshly awarded for a handball by Gonzalo Rodriguez in the 17th minute and Antonio Cassano slotted in a second just after the half hour.
Romulo headed Fiorentina back into the game before half-time and despite having Rodriguez sent off in the 62nd minute, the visitors dominated the remainder of the game and were unlucky not to salvage a point.
Lazio beat Siena 2-1 thanks to first-half goals from Ederson, the Brazilian's first since joining from Olympique Lyon, and Cristian Ledesma, who converted a penalty.
Napoli coach Walter Mazzari was sent off in the first half when he lost his temper after the referee failed to send off Pedro Obiang for a dangerous high tackle on Pablo Cannovaro.
Cavani, who missed a penalty against Lazio, made no mistake in the 67th minute after Marek Hamsik was tripped, the Uruguay forward taking his tally to six in the championship.
In Sicily, Miccoli opened his account by curling a free-kick around the wall in the 13th minute.
Marco Rigone levelled in the 28th minute but Miccoli put Palermo back in front with an individual goal just before the hour and completed the scoring with a volley from near the halfway line which sneaked under the crossbar.
Luigi Giorgi also scored to ease the pressure on Palermo coach Gian Piero Gasperini, whose predecessor Giuseppe Sannino was sacked after only three games at Italy's most volatile club.
The only sour note for Palermo was a red card for Franco Brienza in the 62nd minute.
Around 5,000 fans were allowed to watch Cagliari's game as the Is Arenas stadium, where the Sardinian club has moved this season, was partially opened.
Cagliari's first game was played behind closed doors while their match with AS Roma last Sunday was called off by local authorities after club president Massimo Cellino defied a municipal order not to allow fans to attend.
Roma were awarded a 3-0 forfeit win.
There was little joy, for Cagliari, however as Christian Terlizzi and Vladimir Weiss scored in the second half to put the visitors 2-0 ahead before Mauricio Pinilla pulled one back from a penalty.
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