Noah also supplied five assists and four blocks as Chicago improved to 5-8 in February and pulled a half-game in front of the Nets for the fifth seed in the Eastern Conference.
Carlos Boozer turned in an all-around performance of 20 points, eight boards and five steals in the victory.
Brooklyn, meanwhile, stumbled to its fourth loss in five contests despite 22 points from Brook Lopez.
Toddler uninjured after being knocked over by Obama family dog
Florida bear attack: Black bear mauls woman's face