Joshua Kimmich opened the scoring from inside the box for Germany after 10 minutes, before Ilkay Gündogan added a second from the penalty spot on the stroke of halftime.
Thomas Müller made it 3-0 five minutes into the second half, before two goals in less than two minutes from Timo Werner — the second of which came after a mix-up in the Italian defense — took the game further out of reach for Italy.
Wilfried Gnonto pulled one back from close range when Manuel Neuer’s save was pushed into his path — the 18-year-old’s first goal for Italy — while Alessandro Bastoni’s near-post header from a corner proved a late consolation goal.
The result means Flick is yet to suffer a defeat after 13 games as Germany coach with his side recording a historic first victory against Italy on their 11th meeting.
“We are angry, there are no excuses tonight,” said goalkeeper Gianluigi Donnarumma.
“We have to look each other in the eyes and start again in order to show that this is not the real Italy. We lacked everything tonight.”
It was also a night to forget for England, Italy’s opponent in last year’s Euro 2020 final, after a 4-0 defeat against Hungary at Molineux — Hungary’s first away win against England since 1953.
Despite the Three Lions dominating the opening stages of the match, Hungary took the lead when Roland Sallai scored from a free-kick into the box.
Reece James headed the ball off the line to prevent Hungary getting another goal later in the first half, but Sallai stunned the home side once more on 70 minutes when he slotted in his second.
Things went from bad to worse for England as Ádám Nagy smashed in Hungary’s third, John Stones was sent off for a second yellow card and Dániel Gazdag completed the rout.
The defeat marked England’s second defeat in a row against Hungary and fourth game without a win in this season’s Nations League.
“I picked a very young team, that’s my responsibility,” said head coach Gareth Southgate.
“I haven’t got the balance right in the two games against Hungary. After the first goal, the anxiety crept in a little bit and we weren’t able to recover from that.”
The next round of Group A3 matches take place on September 23 with Italy hosting England and Germany hosting Hungary.