Millsap grabbed nine rebounds, while Williams connected on 8-of-11 attempts from the field for the Jazz, who shot 54.2 percent in racking up their third straight win.
Kobe Bryant scored 34 points for the Lakers, but it wasn't enough as Los Angeles fell to 9-12 overall and 7-6 at home.
Jordan Hill added 17 points with nine rebounds and Jodie Meeks put in 16 off the bench for the Lakers.
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