In a race littered with crashes and safety cars, the young Dutchman kept his composure to top the podium from four-time former champion Sebastian Vettel, who salvaged some pride for Ferrari and delighted the German fans after starting from the rear of the grid.
Russia’s Daniil Kvyat took an unlikely third for Toro Rosso with Canadian Lance Stroll in fourth for Racing Point as the established order was turned upside down.
Championship leader Lewis Hamilton, who started on pole in his Mercedes, initially finished out of the points in 11th, but later 30-second time penalties for Alfa Romeo pair Kimi Raikkonen and Antionio Giovinazzi, saw him salvage two in ninth.
Hamilton saw his victory chances disappear after sliding off the track, losing his front wing and receiving a five-second time penalty for an illegal pit entry following the incident.
His teammate Valterri Bottas looked set to close up in the title race, but crashed out on lap 57 of 64 to complete a sorry afternoon for all-conquering Mercedes.
His spin brought a furious reaction from Toto Wolff, the Mercedes team principal, who was seen banging his fists on the table as the last chance of victory at their home grand prix disappeared
After all the drama, Hamilton has an increased 41-point lead in the title race from Bottas, with Verstappen taking closer order in third, 22 points further adrift.
Before Vettel’s late charge after the fourth and final safety car it looked set to be another dismal afternoon for Ferrari, with his teammate Charles Leclerc careering into the gravel after moving into a good position to challenge for the lead.
The young Monegasque star slumped over his steering wheel in frustration but one lap later Hamilton was to follow him in almost exactly the same spot, losing control of a race he had led from the start with a 35-second advantage at the time of the crash.
Renault’s Nico Hulkenberg also suffered the same fate on the same corner while in fourth place, prompting the third safety car and Leclerc later complained that the low-grip asphalt in that area was “unacceptable” in F1, particularly in the wet. “It’s like a dragster track, very dangerous,” he added.
Hamilton was to eventually make six pit-stops and looked to have finished out of the points for the first time in 23 races.
Running in 12th, Hamilton was heard over race radio asking his engineer Pete Bonnington: “How has it gone this bad?”
Verstappen himself made five pit-stops and survived a 360-degrees spin to win for the second time in three races and for the seventh time overall in F1.
“It was amazing, but really tricky out there,” said Verstappen.
“To make the right calls, you had to be focused. We put on the slick tires and we had a 360! But it was alright.”
Vettel, who crashed out of last year’s German Grand Prix while leading, gained a measure of redemption after equaling his best result of a to date disappointing season.
“It was a long race and at some stages if felt like it was never-ending. I am just very happy.” he said.
For Kvyat, who has endured a topsy-turvy F1 career, it was a double celebration after it was confirmed that he became a father on Saturday night when his partner Kelly gave birth to a daughter.
“It’s amazing to be back on the podium. It was a horror movie with a bit of black comedy out there!” said the Russian, neatly summing up the race.
Behind him there was an excellent fourth for Stroll as his team made a well-timed pit-stop for slick tires in drying conditions, with Carlos Sainz in fifth for improving McLaren and Kvyat’s Toro Rosso teammate Alex Albon in sixth.
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Haas pair Romain Grosjean and Kevin Magnussen took seventh and eighth after the re-classification with Hamilton ninth and Robert Kubica winning a precious point for Williams in 10th after a race that will live long in the memory for its drama and unpredictability until the last.