Los Angeles held the Hornets scoreless for the first 4:48 of the second half to take control and ended a two-game skid.
Bryant began the game needing 13 points to get to 30,000 and join Kareem Abdul-Jabbar, Karl Malone, Michael Jordan and Wilt Chamberlain as those who reached that plateau. Abdul-Jabbar is the league's all-time leading scorer with 38,387.
Bryant reached the 30,000 mark late in the first half and became the youngest player (34 years, 104 days) in NBA history to do so.
New Orleans got 31 points and nine rebounds from Ryan Anderson
The Lakers will end a three-game road trip in Oklahoma City on Friday, play at home against Utah on Sunday and then go back on the road for four more.