The Bulls were clinging to a 3-point lead with 4 1/2 minutes left when Dunleavy sparked an 18-6 run with a long 3-pointer off an assist from Derrick Rose.
He later added a pair of free throws and another jumper, helping the Bulls pull away for the victory.
Carlos Boozer added 17 points and Rose finished with 16 for Chicago.
Kyrie Irving was limited to 5-of-19 shooting for 16 points for the Cavaliers.
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