The PSV Eindhoven forward, 20, struck 11 minutes from time in Hamburg before Georginio Wijnaldum sealed a 4-2 victory which puts Ronald Koeman's side right back in contention in Group C qualifying for next year's European Championship.
Not since November 2002 had Holland beaten their neighbours in their own back yard. That day, they enjoyed a 3-1 success thanks to goals from Patrick Kluivert, Ruud Van Nistelrooy and Jimmy Floyd Hasselbaink.
A controversial penalty scored by Toni Kroos levelled things up before Malen quickly restored Holland's lead and Wijnaldum made sure of victory in injury time.
The win moved Koeman's team to within three points of second-placed Germany with a game in hand.
Lukas Klostermann broke the offside trap and brought a good save from Jasper Cillessen but Gnabry was quickly on the scene to fire home the rebound.
Cillessen was called into action again just before the break, showing terrific reflexes to deny Marco Reus.
It proved an important save as Holland were level early in the second half. De Jong beat Nico Schulz to Ryan Babel's cross before calmly firing past Neuer to score his first senior international goal.
Tah turned Depay's cross into his own net after 66 minutes but Holland's lead was short lived as Germany were awarded a penalty when Schulz's cross deflected off the hand of Matthijs de Ligt – who knew very little about it.
However, the referee pointed to the spot and Kroos calmly sent Cillessen the wrong way. De Jong was incensed and was shown a yellow card after taking his protests too far.
Malen missed a glorious chance to restore Holland's lead straight away but made amends shortly afterwards, with Wijnaldum unselfishly setting up the young forward to volley home.
Germany pushed for an equaliser but in injury time Niklas Sule was caught in possession and Depay broke clear, brilliantly picking out Wijnaldum who put a first-time shot past Neuer.