The Red Bull driver's home triumph from pole position at a soggy Zandvoort equalled now-retired Sebastian Vettel's 2013 streak of success and was the team's 14th consecutive triumph and 13th of the season.
The race started dry before rain caused chaos at the end of lap one, with a dry period followed by a torrential downpour that halted proceedings on the 65th of 72 laps with cars skidding off.
Fernando Alonso (41) put Aston Martin back on the podium with second place and a bonus point for fastest lap after the eventual rolling re-start behind the safety car led to a thrilling final chase.
Pierre Gasly (27) was third for Renault-owned Alpine as Sergio Perez (33), Verstappen's Mexican teammate and closest rival, collected a five-second post-race penalty for speeding in the pit lane and dropped to fourth.
Verstappen now leads Perez by a mighty 138 points with nine races remaining.
"Incredible. They didn't make it easy for us with the weather to make all the right calls. Incredibly proud," said Verstappen as his army of orange-clad fans began the celebrations.
"I already had goosebumps when they were playing the national anthem before the start," added the Dutchman.
"Even with all the bad weather, the rain, the fans are still going at it. So an incredible atmosphere."
Verstappen's 11th victory of the season, and 46th of his career, provided another big push towards clinching a third title well before the end of the season.
Ferrari's Carlos Sainz (28) finished fifth with Lewis Hamilton (38) sixth for Mercedes and fellow-Briton Lando Norris (23) seventh for McLaren.
Alex Albon (27) collected more precious points for Williams in eighth, ahead of McLaren's Oscar Piastri (22) and Esteban Ocon (28) 10th for Alpine.
New Zealander Liam Lawson (21) finished 13th, and ahead of teammate Yuki Tsunoda (23), on his Formula One debut as a replacement for injured Daniel Ricciardo (34) at AlphaTauri.
Lawson also had the thrill of overtaking Charles Leclerc (25) on lap 41 before the Ferrari driver retired with a damaged floor.
CLEAN START
Verstappen led cleanly away at the start with Alonso seizing third place.
Only seven time world champion Hamilton, starting a lowly 13th on the grid, lined up on medium tyres with everyone else on softs but all team strategies were soon shredded as the skies opened.
Perez, seventh on the grid and everything to gain, pitted immediately for intermediates along with six others as the leaders stayed out.
The move paid off for him, but not Ferrari who had Leclerc come in only to find no tyres ready and mechanics scurrying to bring them.
Verstappen came in a lap later but resumed well down the field and set about closing the gap.
He pitted again for dry tyres on lap 11 and took over at the front a lap later when Perez came in and found to his bemusement that his team mate had successfully made the 'undercut' work.
The weather played havoc with others' hopes, Russell plunging from third on the grid to 18th on lap 13 and complaining over the radio.
"I was forecast for a podium. How did we mess this up?" asked the Briton, who climbed back up the order but ultimately retired after collecting a puncture in a clash with Norris after the re-start.
The safety car was deployed from lap 16 to 21 when US rookie Logan Sargeant (22) crashed his Williams into the barriers at turn eight.
Verstappen appeared to be cruising to victory after pitting for intermediates and staying in the lead when the rain returned with 12 laps to go.
The rain was far heavier than at the start and red flags were waved when Alfa Romeo's Guanyu Zhou (24) crashed heavily, the Chinese driver emerging unhurt.
