The 36-year-old is only the fourth player (along with Kareem Abdul-Jabbar, Karl Malone and Michael Jordan) in NBA history to reach the 32,000 mark.
Bryant, who recently set a league record for missed field goals, is 291 points away from catching Jordan at No. 3 the all-time scoring list (32,292).
Bryant reached the mark on a fadeaway, mid-range jumper late in the fourth quarter. He was fouled on the shot and made the ensuing free throw. At the end of the night, his career total stood at 32,001.
Bryant leads the league in scoring at 27.4 points per game. If sustained over an entire season, his 38.9 field goal percentage would be a career low.
Against Atlanta on Tuesday, he scored a game-high 28 points on 10-of-18 shooting in 37 minutes.
The win improved the Lakers' record to 2-9 this season. Los Angeles plays at 9-2 Houston on Wednesday.