Darren Collison had 17 points and 12 assists for the Kings, who took the lead for good in the second quarter.
Chicago was trying to win its first seven road games for the first time in franchise history. Instead they joined the rest of the league with at least one road loss. The last team to start 7-0 on the road was San Antonio, which won its first eight road games in 2010-11.
The Kings held an 88-77 lead when Cousins left the game with his fifth foul with 7:26 left to play. But the frustrated Bulls could never get closer than eight points.
Sacramento has squandered big leads in its last three losses — Dallas (24), Memphis (26) and New Orleans (12), but outscored the Bulls 23-20 in the fourth.
Chicago played without starters Derrick Rose (strained left hamstring) and Pau Gasol (strained left calf) for the second straight game.
Noah picked up his fifth foul at the 4:30 mark of the third quarter after fighting for rebound against Cousins. An incensed Noah stormed to the bench after also being called for a technical.