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McLaren's Oscar Piastri finished second with Ferrari's Carlos Sainz third at Spielberg's Red Bull Ring.
Verstappen finished second while seven-time world champion Lewis Hamilton was third.
Formula One is expected to publish a revamped calendar early next week with a race in neighbouring Hungary, also without spectators, following on from Austria.
The opening race at the Red Bull Ring, belonging to the Austrian energy drink company that owns two of the 10 teams on the starting grid, would be held as planned from July 3 to 5.
The Briton and teammate Valtteri Bottas responded to the 'new normal' resulting from the COVID-19 pandemic by finishing one-two in both free practice sessions on the latest start to a campaign.
The new protocols come into force when the season starts in Austria on July 5.
The Dutchman's victory for the second year in a row at Spielberg also dealt champions Mercedes their first defeat of the season.
Results 1-7
