Pole-sitter Russell delivered an electric start at Interlagos before expertly surviving a late safety car to follow in the footsteps of Hamilton, Jenson Button and David Coulthard and become only the fourth British winner of a grand prix this century.
Russell's supreme performance - 24 hours after he triumphed in Saturday's sprint race - followed another collision between Hamilton and Max Verstappen, with the latter penalised by the stewards.
But the day belonged to Russell, who in his 81st start, fourth season, and first alongside Hamilton at Mercedes, delivered the Silver Arrows' opening win of a turbulent season. Carlos Sainz and Charles Leclerc finished third and fourth for Ferrari, with Verstappen sixth.
"I need some tissues," the 24-year-old Russell said from inside his crash helmet, seconds after the chequered flag fell. "I am crying, boys and girls."
Later, he added: "I was pretty impressed by how quickly I started crying. By Turn 2, I was in floods of tears."
Russell was twice denied a brilliant victory - first through a Mercedes pit-stop mistake and then a puncture - as a remarkable stand-in for a coronavirus-hit Hamilton at the Sakhir Grand Prix almost two years ago.
Here, he looked on course to cruise to the flag only for countryman Lando Norris to throw a spanner in the works when he broke down in his McLaren on lap 55. The safety car was sent out with Norris' machine in a perilous position.
"So, what are we doing?" asked Russell, with Hamilton, who had bounced back from eighth, following his coming together with Verstappen, to second, and now suddenly lurking in his team-mate's mirrors.
"Are we racing? Or securing a one-two?"
"You are racing," replied his race engineer, Riccardo Musconi. "Just be respectful."
With Norris' McLaren out the way, the race fired up again with 11 laps remaining, and Russell delivered another fine restart - his second of the afternoon following a first safety car when Daniel Ricciardo collided with Kevin Magnussen - to leave seven-time world champion Hamilton in his wake.
From there, his victory never looked in doubt. He crossed the line 1.5 seconds ahead of Hamilton as Mercedes completed a one-two finish. Russell now leads Hamilton by 23 points in the standings ahead of next week's concluding round in Abu Dhabi.
"What an amazing feeling," Russell said. "I have dreamt of this moment, many, many times.
"My career has been an emotional rollercoaster. This race was a really tough race. I felt in control. Lewis was super-fast and then, when I saw the safety car, I thought, 'Oh, Jesus, this is going to be a really difficult end.
"He put me under so much pressure, but I am really happy to go home with the victory. I am speechless.
"On the lap back to the pits all of these memories came flooding back, starting off with my mum and dad in go-karting, going through with the support I have had from my family, my girlfriend, my trainer, my manager and then getting on the programme with Mercedes. The list is endless. I am super proud."
Russell's victory means Hamilton is now facing up to the prospect of losing his unique record of winning in every season.
"I want to say a huge congratulations to George," said Hamilton, 37. "What an amazing job. He truly deserves it.
"I am so proud of my team. This is an incredible result. We worked so hard to get a win this season, so this is hugely, hugely deserved."