Verstappen, only 18 and making his debut for the former world champions after being promoted from junior team Toro Rosso a week earlier, beat Ferrari's Kimi Raikkonen, at 36 twice his age by 0.616 seconds.
Verstappen was also the youngest driver to stand on the podium and the first Dutch race winner since the championship started in 1950.
His proud father Jos, who was twice on the podium with Benetton as Michael Schumacher's team mate in 1994 and raced against Raikkonen later in his career, declared it the best day of his life.
"This is really something unbelievably special," he told reporters while others acclaimed an exceptional talent.
Four-time world champion Sebastian Vettel, the previous youngest race winner thanks to his astonishing 2008 Italian Grand Prix victory for Toro Rosso at the age of 21, was third for Ferrari.
Rosberg had his lead trimmed to 39 points, with Raikkonen moving up to second ahead of Hamilton.
