Goals from Toni Kroos, Mario Goetze and Jonas Hector in the first hour gave Italy no chance, with Mesut Ozil then converting a 75th-minute penalty after Sebastian Rudy was brought down.
A more secure defence, with centre-back Mats Hummels playing the full game, meant Italy were made to work hard for a trickle of chances and had to wait until the 84th minute for Stephan El Shaarawy to pull a goal back and deny Germany their biggest victory over their European rivals.
Yet it still equalled their previous best performance against Italy - another three-goal winning margin from a 5-2 victory in 1939.
"We had not won against them for years but tonight we were clever, we defended well and worked hard," said Germany coach Joachim Loew.
"Against England we were missing some of our passion, the final touch, our focus. It was a lesson for us and so we wanted to show tonight that we can be concentrated over 90 minutes."
Germany began as they did against England on Saturday in Berlin, taking a 2-0 lead, with Thomas Mueller, captaining the side for the first time in his 70th international, setting up both goals with crosses from the right.
Kroos drilled home after Mueller's cross was deflected into his path in the 24th minute for his second goal in two matches, and Goetze headed in a fine delivery from his Bayern Munich teammate on the stroke of halftime.
Goetze, overlooked by Bayern Munich coach Pep Guardiola for weeks following his return from injury, did well to sneak in between two defenders to score.
With leading centre-back Hummels substituted at halftime on Saturday, Germany had blown their two-goal advantage against England to lose 3-2. But there was no repeat here, with defender Hector establishing a three-goal cushion with a low shot after some bad defending from the visitors.
Ozil made it 4-0 with his spot-kick before El Shaarawy grabbed a late consolation for the four-time World Cup winners.
"We faced the best team in the world," said Italy coach Antonio Conte. "It was an important game in terms of evaluating our team. There is a gap we need to close.
"These tests were used to see the state of the team and make sure we are competitive, and now we have to make our assessments."
Italy, who drew 1-1 with Spain in a friendly last week, face Belgium, the Republic of Ireland and Sweden in the group stage of Euro 2016.
(Reporting by Karolos Grohmann, editing by Stephen Wood)
Share
