Red-hot Fiorentina replaced Inter Milan as Serie A leaders by cruising to a 3-0 home victory over Atalanta on Sunday.
Lorenzo Insigne struck twice and set up another as Napoli romped to a 4-0 win over AC Milan at the San Siro.
Napoli made it three wins out of three for Italian sides in the Europa League on Thursday night with a 2-0 victory at Legia Warsaw.
Juventus' poor Serie A start continued with defeat at Napoli, while Roma returned to winning ways against struggling Carpi.
Juventus could only draw 1-1 at home to Frosinone in Serie A on Wednesday, as leaders Inter Milan beat Hellas Verona 1-0.
A Gonzalo Higuain-inspired Napoli ran riot against Lazio while there were also wins for Inter Milan and Fiorentina.
There were wins for Napoli, Borussia Dortmund and Marseille on matchday one of the Europa League.
Mario Balotelli hit the post as AC Milan lost 1-0 to leaders Inter in Serie A on Sunday, while Torino remain unbeaten.
Nat Chalobah has chosen an "interesting challenge" in joining Napoli on loan, according to his England U21 boss.
Jonathan de Guzman's proposed loan move to Bournemouth is now unlikely to happen, according to Sky sources.
Norwich are locked in negotiations with Napoli for their centre-back Kalidou Koulibaly, Sky sources understand.
Bournemouth and Sunderland are competing to sign former Swansea midfielder Jonathan de Guzman, Sky sources understand.
Serie A champions Juventus saw their 47-match unbeaten home league record come to an end against Udinese.
Southampton are interested in Napoli defender Kalidou Koulibaly, according to Sky sources.
Leicester have completed the signing Napoli midfielder Gokhan Inler on a three-year deal.
Leicester are close to completing the signing of Napoli midfielder Gokhan Inler, according to Sky sources.
Vlad Chiriches is set for a move to Napoli with Sky sources reporting the Tottenham defender is in Italy for a medical.
Watford have completed the signings of Uruguayan defender Miguel Britos and Spanish midfielder Jose Manuel Jurado.
Argentina striker Gonzalo Higuain will not be leaving Napoli, according to club president Aurelio De Laurentiis.
Unai Emery claims he rejected offers from West Ham and Napoli to extend his contract with Europa League winners Sevilla.