Spanish winger Ferran Torres scored a hat-trick in Seville in a major contribution to his team's victory.
Alvaro Morata, Rodri and Mikel Oyarzabal were the other scorers for Spain.
German midfielder Toni Kroos said his team was surely bothered by the loss and praised their opponents for their attacking skills.
"It's probably not the most bitter defeat of my career, but surely one of the biggest. It hurt. We did not get any grip on them. Spain showed us how to attack," Kroos said after the match.
Germany last lost 6-0 to Austria in 1931, and Tuesday's loss is now among the Germans' heaviest defeats in history.
Hungary thrashed Germany 8-3 in the 1954 FIFA World Cup as the margin was five goals.
Spain advanced to the Nations League finals, winning Group 4 with 11 points.
Germany was in second place with 9 points.
The heaviest defeats for the German men's team. (Note that the current team counts as the successor to West Germany.)
0-9 March 13, 1909 in Oxford against England
0-6 May 24, 1931 in Berlin against Austria
0-6 November 17, 2020 in Seville against Spain
3-8 June 20, 1954 in Basel against Hungary
0-5 September 13, 1931 in Vienna against Austria
Heaviest defeats under coach Joachim Löw:
0-6 November 17, 2020 in Seville against Spain
0-3 October 17, 2007 in Munich against the Czech Republic
0-3 October 13, 2018 in Amsterdam against the Netherlands
