The former English youth international Jamal Musiala opened his account for the Germans, ran into the goal and swept home confidently.
In the second half, Kai Havertz scored the first goal after a selfless pass from Thomas Müller.
Timo Werner shot second place after Müller’s great flick and also rolled into a wonderful third place.
The Germans could have had more, but Chelsea striker Werner rattled the post with a knocking low drive just before half-time but managed to score two goals as his team got the job done with a clinical finish in the second period.
It will be an unforgettable night for 18-year-old ex-Chelsea Academy graduate Musiala, who played 19 times for various English youth teams but declared that he was playing for Germany through his mother when he scored his first goal for Germany in his ninth international match A national team scored.
Hansi Flick’s men, who are four-time world champions, have reached the tournament for the 20th time, only Brazil (21) competes more often.
They made it with two games to go, against Liechtenstein and Armenia next month.