Kyrie Irving scored 26 to lead Cleveland, which has dropped the first two games of a five-game homestand. The Cavs have lost all of their momentum after going 3-2 on the road.
"We're not making any excuses here," Irving said. "We've got to pick it up."
Although they were missing two starters in Boozer (calf) and Hinrich (hamstring), the Bulls had more than enough to hold off the Cavaliers.
Making just his fourth start, Gibson scored 12 in the third as the Bulls opened a 71-62 lead entering the fourth.
Dunleavy's 3-pointer extended Chicago's lead to 12 in the opening minute of the final quarter, but the Cavs fought back behind Dion Waiters and pulled to 84-81 on his 3. However, Dunleavy scored again, Noah made a layup and Augustin buried a 3-pointer to give the Bulls a 91-81 lead.
The Cavs were still within 93-87 when Dunleavy knocked down another 3-pointer with 38 seconds left to seal Chicago's win.
Dunleavy added 22 points for the Bulls, who got just four points from their bench.
Waiters had 15 for Cleveland.
Deng spent 10 seasons with the Bulls, and the 28-year-old knew it would be challenging to oppose his ex-teammates.
"It's definitely going to be weird because it's guys I'm really close with and it feels like just yesterday I was going to battle with them and now I'm going against them," he said at the morning shootaround.
Following the game, Deng acknowledged it was difficult to face players he knows so well.
"I tried to really play the game within myself," he said. "They played good D. I missed shots. I'm not happy with my performance. That's a good defensive team. We've just got to keep growing."
Before the opening tip, Deng ran over to Chicago's bench and hugged Thibodeau and shook hands with all of the team's assistant coaches.