Mike Dunleavy added 16 and DJ Augustin 12 for the Bulls.
Isaiah Thomas led the Kings with 26 and DeMarcus Cousins had 25.
Both teams struggled on offense, with the Bulls shooting 40 percent and the Kings 37 percent.
The Bulls, who are fourth in the Eastern Conference, improved to 3-2 on their six-game homestand. The Kings are 2-4 on their seven-game road trip.
Cousins hit a layup with 1:01 left to cut the Bulls’ lead to 88-85.
Gibson responded with a jumper and the Bulls made four of six free throws to seal the win.