In the first Formula One race in Mexico for 23 years, the 30-year-old German made light of the altitude of more than 2,000 metres and his anger at the manner of Hamilton's successes by leading, bar the pit-stops, from the 20th pole position of his career to the chequered flag.
It was his fourth win of the season and 12th of his career.
"What an amazing day, it was a great battle with Lewis, who drove really well and I am really, really happy with this win - and what a place to do it, in front of an absolutely awesome crowd," said Rosberg on Sunday.
"Nico drove a fantastic race," said the Briton.
Hamilton, who started second, was never able to mount a serious challenge to win the race in front of a crowd of 140,000 and came home behind his team-mate to confirm the overall dominance of the champion team.
For Rosberg, it was a richly satisfying triumph seven days after he had thrown away victory with an error in the United States Grand Prix where Hamilton won, after a wheel-banging duel on the opening lap, to confirm his third drivers' world championship.
Rosberg, clearly delighted by his success after securing only two wins from 10 pole positions, came home 1.9 seconds clear for his first win since the Austrian Grand Prix.
Bottas of Williams, also powered by Mercedes, came home third ahead of Daniil Kvyat of Red Bull, his team-mate Daniel Ricciardo and Felipe Massa in the second Williams.
Nico Hulkenberg finished seventh ahead of his Force India team-mate local hero Sergio Perez, teenager Max Verstappen of Toro Rosso and Romain Grosjean of Lotus.
In warm sunshine with a track temperature of 56 degrees Celsius, there were widespread fears about brakes overheating before the lights went out.
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