The Germans are now on nine points, three behind group leaders Northern Ireland, who have four wins from four but needed an 86th minute winner by Paddy McNair to edge past hosts Belarus 1-0.
Germany got off to an explosive start and two goals from Marco Reus and one from Serge Gnabry, Leon Goretzka and Ilkay Guendogan's penalty saw them kill off the game by the 37th minute.
Their quick, flowing football gave their opponents no chance even when they piled 10 outfield players into the box.
Reus' second goal, a superb free kick from 20 metres, was Germany's first free kick goal since 2007.
Gnabry then grabbed his second goal after the break before Timo Werner and Leroy Sane also got on the scoresheet in a completely one-sided encounter that also confirmed Germany's improving form.
The Germans are looking to rebuild after their woeful World Cup first round exit last year along with their Nations League relegation. They also beat Belarus 2-0 on Saturday.
"We wanted to score more goals than we did against Belarus and we managed that," Reus, who also hit the woodwork, told reporters.
"We did it very well in the opening half hour, we had really good rhythm and our passing game was outstanding."
Germany next play Netherlands on Sept. 6 while Northern Ireland, who have won four games in a row at the start of a qualifying campaign for the first time, host Germany on Sept. 9.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
