Joachim Low felt his Germany side showed they had learned the lesson from their disappointing defeat to England after his side thrashed Italy 4-1 on Tuesday.
First-half goals from Toni Kroos - his second in as many matches for his country - and Mario Gotze put the hosts 2-0 up at the break in Munich.
They had found themselves with the same lead against England on Saturday in Berlin, only to end up losing the game 3-2.
However, they did not make the same mistake again, adding further goals after the interval from Jonas Hector and Mesut Ozil to run out winners against Italy for the first time since 1995.
"We've not had something like this against Italy for a long time, but we played clever, defended well and attacked well. It was a good game from us tonight,'' Low told ARD television.
"All of our players fulfilled their jobs really well.
"We were beating England 2-0 and we just lacked that concentration to go the distance and we were taught a lesson.
"Tonight we wanted to show we can concentrate for the full game and be disciplined and we did that.''
Low was particularly pleased for Gotze, who has only just returned to action after overcoming a groin injury suffered in October 2015.
The Bayern Munich player headed home a cross from club colleague Thomas Muller to double Germany's lead on the stroke of half-time.
"Gotze has been out a long time injured and I can understand why he has not been playing so much for Bayern, because they've got a strong side,'' Low added.
"But he's been training extra hard in recent weeks, putting in extra hours at the training field and I hope this gives him a bit of self-confidence for the coming weeks.''