Germany bounced back from defeat by England on Saturday to beat Italy for the first time in almost 21 years.
The world champions avoided a third straight loss as Toni Kroos opened the scoring before reported Liverpool target Mario Gotze doubled the lead.
Left-back Jonas Hector, another rumoured Liverpool option, then scored a header with a Mesut Ozil penalty making it 4-0 with 15 minutes left.
Stephan El Shaarawy grabbed a late consolation for Antonio Conte's team.
