Boozer connected on 10-of-15 shots and hauled down 19 rebounds. Hamilton went 10-for-10 from the free-throw line.
Luol Deng (14 points, eight rebounds) and Kirk Hinrich (10 points) also reached double figures for the Bulls, who improved to .500 (6-6) with the win -- their ninth straight over the Bucks.
Brandon Jennings pumped in 23 points for Milwaukee before appearing to sprain an ankle with 23.1 seconds left in the contest.
Monta Ellis supplied 17 points in Milwaukee's third straight setback.