Rose, the reigning NBA MVP, hit an incredibly tough floater from a bit inside the free-throw line over Lakers forward Pau Gasol with 4.8 seconds to play in the fourth quarter to give the Bulls an 88-87 lead.
Bryant then drove to the basket for the winning points, but was blocked by a swarming Bulls defense in the paint as time ran out.
Chicago trailed during the fourth quarter, but closed out the game with solid offensive play and proved they could defeat an elite NBA team even when they don't play to the best of their abilities.
Rose had a very good game and was quite efficient offensively. He shot 9-of-13 from the field including 4-of-6 from beyond the three-point line to lead the Bulls with 22 points.
Chicago got just 18 points from its bench so it was critical that the starters play well and the team as a whole play very well defensively.
The Bulls have high expectations this season after they lost in the Eastern Conference finals to the Miami Heat last year in five games.
The team added former Detroit Pistons shooting guard Rip Hamilton in free agency to shore up some weaknesses at guard, but he scored just six points on 3-of-8 shooting in his Bulls debut.
Despite the team's struggles, the Bulls should be proud of their win against the Lakers on Sunday. They did not play very well in the second half, but found a way to win with the game on the line against an experienced team with a championship pedigree.
This win will give the Bulls a lot of confidence moving forward and once again proved that the team is at its best when they commit to playing strong defense for 48 minutes.