The Bulls held a 50-43 halftime advantage, but broke the game open with a 14-2 run to end the third quarter, which made their lead 73-57.
The closest New York would come was 84-71 after Zack Randolph hit a bank shot with 5:13 left in the fourth.
Luol Deng had 17 points and seven assists, while Joe Smith and Kirk Hinrich scored 13 points apiece for the Bulls, who rose to 2-1 since Jim Boylan took over as interim coach from the fired Scott Skiles.
In his first start, Nate Robinson led New York with 19 points and five assists.
Randolph had 18 points and 12 rebounds, and Quentin Richardson scored 13 points for the Knicks, who have lost 10 of their last 12 games.
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