Bryant entered the contest at 31,973 points, needing just 27 more to reach a milestone that had previously only been achieved by Kareem Abdul-Jabbar (38,387 points), Karl Malone (36,928) and Michael Jordan (32,292).
Having scored 27 or more points in six of his first 10 contests this season, Bryant was a good bet to hit the 32,000-point mark in Tuesday's game, which came just two days after his 44-point performance in a loss to the Golden State Warriors.
Bryant wasted no time moving toward the milestone Tuesday night, scoring 11 first-quarter points to help the Lakers build a 31-20 lead at the end of the first period.
Following another eight points in the second quarter, Bryant entered halftime just eight away from the milestone.
What once looked like a sure thing wasn't so certain after the third quarter, as Bryant didn't score a single point in the frame, missing his lone field-goal attempt.
However, he came back from the bench strong midway through the fourth quarter, entering the game with just over six minutes remaining and the Lakers holding a 97-92 lead.
As he has done so many times before, Bryant shut the door with a huge finish, scoring nine of his team's final 17 points in the victory.
Point No. 32,000 was especially impressive, as Bryant was sitting at 31,998 with his team up 105-102 in the final 90 seconds, and he then hit a deep two-point jumper over Hawks guard Thabo Sefolosha, who was called for a foul on the play.
Following the successful free throw, he sat at 30,001 career points, leaving him just 291 shy of Jordan for third place on the all-time list.
Bryant figures to pass His Royal Airness sometime before the New Year, assuming his health is cooperative.