The Mexican triumphed in a rain-delayed race that saw Ferrari's Charles Leclerc finish second.
The Dutchman won his fifth race in a row and 11th in the season.
Lewis Hamilton finished second for Mercedes.
Seven times world champion Lewis Hamilton finished second.
Verstappen finished second while seven-time world champion Lewis Hamilton was third.
The Mexican's teammate Max Verstappen finished third to stretch his Formula One championship lead over Leclerc.
The win ahead of Mexican team mate Sergio Perez completed a hat-trick for Verstappen.
The Dutchman crossed the line just half-a-second ahead of Leclerc, who keeps the championship lead.
The Monegasque, who started from pole, crossed the line 5.5 seconds ahead of Spaniard Sainz.
The Mercedes and Ferrari drivers were back with their teams at the Red Bull Ring on Thursday ahead of this weekend's Styrian Grand Prix on the same track where they finished first and second respectively on Sunday.