Starting in second position, behind Rosberg in pole, Hamilton was able to overtake and win the race at the Hungaroring circuit in Budapest, reports Efe.
The win is Hamilton's fifth in Budapest, his previous record of four wins being shared with retired German driver Michael Schumacher.
With 25 more points -- bringing him up to a total of 192 -- Hamilton leads the driver standings for the first time this season, and knocks Rosberg off the top spot.
Sunday's win puts Hamilton 6 points ahead of Rosberg, who finished second in the eleventh stage of the Championship.
Completing the podium in third was Australian driver Daniel Ricciardo (Red Bull).
Sebastian Vettel of Germany (Ferrari) came in fourth.
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