The Lakers had defeated the Bulls seven straight times, but Chicago overcame a 10-point first quarter in a defensive battle and opened as much as a 13-point lead with 4:30 to play.
Chicago, a winner of four in a row, shot only 41 percent from the floor but made 8-of-17 from 3-point range. Three of the long-range shots came from Kyle Korver, who scored 13 points off the bench.
Rose had nine assists to go with his 29 points.
Bryant made just 9-of-23 shots and scored 23 points in the Lakers' lowest point production of the season. They had a three-game winning streak snapped.
Bryant, however, did move into 11th place on the NBA's all-time scoring list with 26,398 points. He passed John Havlicek, who had 26,395. Bryant needs 270 points to catch Dominique Wilkins for 10th place.