The 26-year-old Briton came home 0.526 seconds ahead of the seven-time world champion, who controlled most of the race before being called in for a second stop, with McLaren's Oscar Piastri finishing third, just 1.173 seconds adrift of Russell.
Russell drove the 44-laps race with only one pit stop which led to him going 34 laps on his second set of tyres, a strategic decision taken during the contest enabling him to take the lead and an unexpected third career victory.
"Amazing, amazing result," shrieked Russell.
"We definitely didn't predict this in our strategy meeting this morning but the car was awesome. We changed a lot on Friday night and the tyres felt great.
"I kept saying 'I think we can do the one-stop, I think we can do the one-stop' and the strategy was a really great job.
"Well done to Lewis as he really controlled that race and if circumstances were slightly different, I'm sure he would have got the victory.
"One-two for the team was awesome and what a way to go to the break."
Russell's win also brought Mercedes a third win in four races following a poor run of results in the last two years.
"We had such a disaster on Friday when the car was nowhere," said Hamilton, who led for most of the race until Russell’s strategy undercut the field.
"We made some changes and it was difficult to know in the wet yesterday, but the car was fantastic. Congratulations to George and the team."
Ferrari's Charles Leclerc, who started on pole position, came home fourth ahead of three-time world champion and series leader Max Verstappen of Red Bull, Lando Norris in the second McLaren and Carlos Sainz in the second Ferrari.
Sergio Perez, who started second, finished eighth in the second Red Bull ahead of two-time champion Fernando Alonso of Aston Martin and Esteban Ocon of Alpine.
Pit stop strategy
After Saturday's deluge, the race began in bright, warm and dry conditions.
Leclerc enjoyed a smooth start from pole as Hamilton beat Perez to take second into La Source, where they battled wheel to wheel.
Norris had a poor start and ran through a gravel trap, falling to seventh behind Russell and Sainz as the early order settled while Verstappen gained two places to rise to ninth, having started 11th due to a 10-place penalty for taking an additional new engine.
Hamilton's pace took him within reach of Leclerc on lap three when, using Drag Reduction System (DRS), he swept into the lead on the Kemmel Straight.
He stayed there and by lap five led Leclerc by a second ahead of Perez, Piastri and Russell with Sainz sixth, the only top 10 driver on hard tyres, ahead of Norris and Verstappen.
Russell and Verstappen came in after 10 laps, both switching from mediums to hards and re-joining in 13th and 14th respectively before Hamilton, Perez and Piastri pitted one lap later.
Norris finally pitted on lap 16, rejoining eighth behind Verstappen with whom he battled until the end of the race.
With all of the other contenders pitting a second time, Russell became the fifth race leader and opted to stay out on the one-stop strategy.
Hamilton closed but instead of waving his teammate through Russell was give the all-clear to race him, a potentially dangerous strategy from Mercedes as a flying Piastri quickly closed on them.
With five laps to go, Hamilton was two seconds behind Russell and Piastri 5.4 adrift, the top three setting up a grandstand finish that saw Piastri close up to within two seconds while the Mercedes men tussled to the flag.
"I thought I could catch them but clean air made such a big difference today," said Piastri.
Verstappen still leads the championship race with 275 points, 78 clear of Norris. Red Bull top the constructors' championship 42 points ahead of McLaren.
Formula One now heads into a summer break with the next race in Zandvoort for the Dutch Grand Prix on August 25.
