Liverpool defender Van Dijk pounced to nod home the loose ball on the half-hour mark after Ryan Babel had struck the crossbar with a header after a corner from Depay.
Germany had chances to grab a leveller after the break, with substitute Leroy Sane steering a glorious opportunity wide.
It was also denied what appeared to be a clear-cut penalty in the final 10 minutes when Arnaut Groeneveld tripped Matthias Ginter.
However, Depay added an 86th-minute second on the counter-attack and Liverpool midfielder Wijnaldum rifled in a third in stoppage-time, securing Oranje's biggest ever win over Germany.
It leaves Low's side in danger of relegation in League A Group 1, where it sits bottom, having drawn 0-0 with France in its first game.