Hamilton outpaced Rosberg at the start and then controlled the 70 laps with a mixture of speed and flawless judgement in sweltering heat at the Hungaroring circuit.
His victory completed a hat-trick of successes in consecutive races, was his outright record fifth in Hungary, his fifth of the season and the 48th of his career.
Decision of the IOC Executive Board concerning the participation of Russian athletes in the Olympic Games Rio 2016 https://t.co/wfe08HKEqF
— IOC MEDIA (@iocmedia) July 24, 2016
Rosberg, who started from pole position, came home second ahead of Daniel Ricciardo of Red Bull, four-time champion Sebastian Vettel of Ferrari and Dutch teenager Max Verstappen in the second Red Bull.
Hamilton in hunt for Russia hat-trick
Kimi Raikkonen was sixth in the second Ferrari ahead of two-time champion Fernando Alonso of McLaren and Carlos Sainz of Toro Rosso, Valtteri Bottas of Williams and Nico Hulkenberg who was 10th for Force India.
Hamilton's win increased his points total to 192, six more than Rosberg as Ricciardo moved up to third.
"Awesome race Lewis, mega result," said his Mercedes engineer on team radio. "Well done mate. Fantastic drive."
Hamilton responded generously. "As always, thank you guys, so much, for your hard work all weekend. This is a great result for the team," he said.
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