The Bulls shot 33.0 percent from the floor as a team, including 3-of-17 from three-point territory.
Nate Robinson cut the Hornets' lead to four on three different occasions late in the fourth quarter, the last time at 81-77 with 1:16 left in the game, but that's as close as Chicago would get. New Orleans led for the entire fourth quarter to secure the win.
The Bulls were led by Luol Deng, who had 19 points and eight rebounds on 6-of-15 shooting from the field.
Ryan Anderson started in place of Davis and had a double-double with 12 points and 13 rebounds.
New Orleans improved to 2-1 on the season with the win.