A jump shot by Tyreke Evans brought the Kings within 86-83 with 43 seconds to play, but Chicago held on at the foul line while opening defense of its Central Division title.
Noah made two free throws with 24 seconds left to boost Chicago's lead to 91-85 and then accounted for the final score by hitting two more with 15 seconds remaining.
Evans scored 21 points in leading Sacramento.
Dog comes home gnawing on human bone
Julius Randle breaks leg during NBA debut