Andrei Kirilenko brought Utah within a point by making a free throw with 1:28 to play, but the Jazz did not score again.
Rose gave the Bulls a three-point lead with his two foul shots and Brewer finished the scoring by making two more with 7 seconds to play.
Rose scored 29 points and Carlos Boozer, in his first game against his former team, had 14 points and six rebounds.
Boozer played six seasons with Utah and was a two-time all-star with the Jazz before signing with the Bulls last summer. He missed the start of the season with a broken hand and has played in 33 of Chicago's 51 games.
Utah was led by Al Jefferson with 26 points and eight rebounds. The Jazz lost their third straight home game.
2014: The Year in Music [PHOTOS]