Russell started from pole position on Saturday, quickly built a gap to Lando Norris in second and managed the pace from there, taking his first win since the Austrian Grand Prix in June.
"Obviously a great start to the weekend," he said.
Charles Leclerc snatched second off Norris with a daring pass into the inside of the first corner with six laps to go, but couldn't get close enough to try passing Russell.
Norris held off a late charge from Russell's Mercedes teammate Kimi Antonelli to stay third as the Italian pulled out of a potential overtaking move on the final lap.
"We just don't have the pace in general, especially in the slow-speed corners," Norris said.
Fourth-placed Antonelli, starting fifth after car damage in qualifying, extended his standings lead by three points to 53 because his closest challenger, British driver Lewis Hamilton, could only manage seventh for Ferrari.
F1 still hasn't had a wet race this year but came tantalisingly close as rain fell as the drivers were heading back to the pits, seconds after the sprint finished.
"If there was one more lap it would have been a very, potentially, different end to the race, so I'm glad the rain came when it did," Russell said.
Australia's Oscar Piastri finished fifth in the sprint race.
Qualifying takes place later on Saturday for Sunday's Dutch Grand Prix.
15°C