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Ferrari's Charles Leclerc finished second to split the Red Bulls at their home circuit with Sergio Perez completing the podium at Spielberg.
This was double world champion Verstappen's seventh win out of nine this season and his fifth successive victory.
Perez has won the other two races.
It followed the Dutchman's success in Saturday's sprint and with the fastest lap gave him a maximum 34 points from the weekend.
"That is the full sweep, classy Max, very very classy," said Red Bull boss Christian Horner over the team radio.
"The car was on fire!" replied Verstappen.