It leaves Low's side in danger of relegation in League A Group 1, of which they are bottom, having drawn 0-0 with France in their first game.
It was the sixth defeat in 10 games for Low's side, who went out at the group stage of the World Cup in Russian Federation. "We had our chances, which we didn't put away, and had control of the game", the German FA website reported him as saying. The fact is, we had so many chances in the last two games but couldn't score.
Germany now face world champions France in Paris on Tuesday and Loew can ill afford another heavy defeat.
European worldwide football has a handful of truly special games and one of those is undoubtedly between the Netherlands and Germany, a rivalry which dates back to the Second World War and was played out on Saturday with the Dutch emerging as unlikely 2-0 winners.
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Van Dijk opened the scoring with a well-taken header after Ryan Babel had headed against the crossbar on 30 minutes.
Since the end of their World Cup qualifying campaign in October 2017, Germany have won only three of their past 12 matches - a 2-1 success in the finals against Sweden and two victories in friendlies against Saudi Arabia and Peru.
Manchester City forward Leroy Sane, on as a second half substitute, should have equalised but he dragged a shot just wide when unmarked eight yards out.
Depay then compounded Germany's misery by stroking home a pass from Quincy Promes three minutes from time after the pair got in behind the defence.
And Wijnaldum added a third soon after.