The four-time world champion claimed his second victory of the season and 41st of his career -- drawing him level with the late Brazilian legend Ayrton Senna in equal third on the all-time list -- after leading from the start to dominate a thrilling and unpredictable contest.
The Red Bull pair of Russian Daniil Kvyat and Australian Daniel Ricciardo finished in second and third respectively.
The ferocity of the contest, lit up by Vettel's blazing speed and tenacity, served as an appropriate tribute to Frenchman Bianchi, who died on July 17 from injuries sustained when he collided with a recovery vehicle in torrential rain at last October's Japanese Grand Prix.
"Merci Jules, c'est a toi," said the winner. "Thank you Jules, You will always be in our hearts... This win is for you."
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It was Vettel's first victory in Hungary, and 21-year-old Kvyat's first career podium - the best ever by a Russian driver -- as Red Bull produced a reminder of their pedigree. It was the first podium this year without a Mercedes driver.
Series leader and defending two-time champion Briton Lewis Hamilton finished sixth, after starting from pole position, for Mercedes to enlarge his advantage in the title race after an afternoon of incidents, mishaps and penalties.
Inspired, perhaps, by the team's call for total commitment to racing in a signal of respect for Bianchi, Vettel surged from third on the grid to pass Rosberg into Turn One.