Mauro Icardi inspired a superb comeback win for Inter as they beat Juventus 2-1 on Sunday, while Roma lost at Fiorentina.
Inter Milan suffered a surprise 2-0 defeat to Chievo on the opening weekend of Serie A while Napoli also struggled.
Juventus celebrated winning the Serie A title for the fifth year in a row by beating relegation-threatened Carpi 2-0.
Hellas Verona beat AC Milan but Carpi's 1-0 victory over Empoli confirmed relegation from Serie A for Luigi Delneri's side.
Paulo Dybala scored twice as Juventus thrashed Lazio 3-0 to take what could prove to be a decisive lead in Serie A.
Liverpool target Piotr Zielinski has claimed he has held talks over a potential summer move to Anfield.