The Mercedes driver won ahead of Red Bull's Max Verstappen of the Netherlands.
Russell started in pole position after a controversial qualifying session where he set the fastest lap time under yellow flags after Verstappen crashed.
He maintained the lead throughout the race, but Verstappen closed in at the end without getting all the way to the finish line in the heatwave in Spielberg, where it was 35 degrees Celsius. In the end, the difference was 1.6 seconds.
The victory was Russell's first since the World Championship opener in Australia in March.
World championship leader Kimi Antonelli of Italy/Mercedes finished third.
Lewis Hamilton and Ferrari were unable to build on their victory last time out, and the seven-time world champion finished fifth.
