The Bulls outscored the Cavaliers by 16 points in the first period and there was never any hint of a rally from Cleveland, which has split its opening two games of the campaign.
Chicago shot a sizzling 63 percent from the field with Boozer making 7-of-11 and Hamilton going 8-of-12. The Bulls have captured their first two games this year after opening the season with a win at home against Sacramento.
Kyrie Irving led Cleveland with 15 points while Alonzo Gee and Anderson Varejao both had 12.
Hamilton hit a 3-pointer to finish off a 7-0 run that started the game and the Bulls built a 25-point halftime lead.
Chicago has defeated Cleveland in their last nine meetings. Cleveland will now embark on its longest road trip of the season, a six-game affair that begins Saturday in Milwaukee.