Ronald Koeman's men had seemed certain to finish second behind France in Group 1 of League A when Timo Werner's first international goal since June and Leroy Sane's second in as many outings had Germany coasting.
Needing only a point to advance, Quincy Promes offered a late lifeline to the outplayed visitors as he cut the deficit in half before makeshift striker Virgil van Dijk completed a remarkable turnaround in the 90th minute with a volley.
The final result was an extension of Germany's annus horribilis as Netherlands rescued a dramatic draw to advance to the final four.
Germany's chance to add a positive finish to a miserable 2018 began brightly as RB Leipzig striker Werner rifled Serge Gnabry's flick-on into the bottom-left corner in the ninth minute.
Toni Kroos helped create the opener and next provided the lofted pass from which Sane doubled the advantage, the Manchester City man regathering possession and beating Jasper Cillessen courtesy of a deflection off Kenny Tete.
Netherlands' hopes appeared to be fading when Ryan Babel limped off clutching his hamstring and his replacement, Javairo Dilrosun, lasted only 20 minutes of the second half before a similar issue curtailed his debut.
Werner had earlier dragged a promising opportunity past the far post, while substitute Marco Reus failed to tee up Sane for a tap-in amid a period Germany would come to rue.
Promes punished some poor defending in the 85th minute and captain Van Dijk then sucked the life out of substitute Thomas Muller's 100th international appearance for Die Mannschaft.
The defender's expert volley from Tonny Vilhena's cross miraculously sent Netherlands through at France's expense and condemned Joachim Low's side to a fifth competitive fixture without victory.
UEFA Nations League (@UEFAEURO) November 19, 2018
What does it mean? Winning mentality lacking for Germany
What seemed likely to be a lesson of the established order for Netherlands became a reminder of just how much Germany's identity has been lost in recent months.
Low can no longer rely on the heroes of 2010 and yet, for now, he must tread patiently in troubled waters as the emerging generation seeks to discover the competitive nous of the great teams that have preceded them.
Van Dijk the darling of Dutch football
It seems there is little Van Dijk cannot do at the moment as, even during a match in which his side had been breached twice, the defender managed to conjure a moment of inspiration when it mattered most.
Marco van Basten would have been proud of that volley.
Goretzka learns heavy lesson
All Leon Goretzka had to do was toe the ball away from harm on the edge of his penalty area and Germany would have been home and dry.
Instead, the Bayern Munich midfielder was carelessly robbed of possession and Promes was eventually able to curl in the goal that made the stunning late scenes possible.