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Hamilton now has 250 points, with team mate Valtteri Bottas on 188 and Verstappen closing in fast on 181.
Russian Daniil Kvyat was an astonishing third to hand Red Bull's sister team Toro Rosso their second ever podium.
It was Hamilton's seventh win in 10 races this season and 80th of his career.
Eight climbers - four from Britain, two from the United States, and one each from Australia and India - went missing on May 31 after they failed to return to their base camp near the 7,816 metres (25,643 feet) mountain, Nanda Devi.
The Dutchman's victory for the second year in a row at Spielberg also dealt champions Mercedes their first defeat of the season.
The five-times world champion now has 79 career wins, 12 short of Michael Schumacher's all-time record with 13 races remaining this season.
Apparently the mountaineers were perished in an avalanche while ascending an unscaled peak near the Nanda Devi East peak after they failed to scale the latter.
Ferrari's Sebastian Vettel was runner-up, ending Mercedes's run of five successive one-two finishes, with Hamilton's team mate Valtteri Bottas third.
The three-time Formula One champion regarded as one of the finest racers of all time and who later became a successful airline entrepreneur, has died at 70 after battling declining health.
The Briton took an extra point for the fastest lap of the race.