They now sit bottom of their UEFA Nations League group with one point, behind the Dutch and France - who will be looking to pile the pressure on when they meet the Germans in Paris on Tuesday.
For Low's team, the defeat continued an alarming slump which saw the team exit the World Cup in Russian Federation at the group stage despite being defending champions.
"The young Leroy Sane and Julian Brandt were a breath of fresh air, but they missed a couple of good chances, maybe due to their inexperience", said Low. Why are we not scoring?
This is the first time the Dutch have beaten Germany for 16 years and the comprehensive defeat leaves Loew under increasing pressure to resign after 12 years in charge. Neuer was at fault for the first Dutch goal, coming off his line and getting lost when Memphis Depay whipped in a corner which Ryan Babel headed against the bar.
Depay then sealed the points moments before the final whistle, finishing off a swift counter-attack with a cool finish from close range.
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The last goal Germany scored in a competitive match was Toni Kroos' memorable last-gasp victor against Sweden at the World Cup this summer.
After van Dijk's opener, the Dutch had chances to double their lead but Wijnaldum shot wide and Depay headed off target.
That miss proved costly, as with Germany pushing for an equaliser, they gave the ball away and Promes played in Depay for the second goal.
He said his team had paid the price for failing to take their chances and accused them of falling apart as Depay and Wijnaldum struck in the closing minutes.
The defending World Cup champs got two goals from Antoine Griezmann, and Germany saw defeat for the sixth time in the last 10 games.