Williams canned five 3-pointers and dished out eight assists while Kris Humphries contributed a double-double of 24 points and 18 rebounds for the Nets, who led wire-to-wire.
MarShon Brooks added 19 points as New Jersey used a tough defense to hold the Bulls to 39.3 percent (33-of-84) for the game.
Chicago, meanwhile, played without star guard Derrick Rose for the fifth consecutive game. The reigning NBA MVP was listed as day to day with a sore back.
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