The Los Angeles Lakers star, now in his 19th season, passed the Chicago Bulls legend (32,292 points) and the player to whom he has long been compared with a free throw in the second quarter against the Minnesota Timberwolves at the Target Center.
"I'm just honored to be here, man, to still be playing," Bryant said. "I appreciate being able to play this long. Careers normally don't last this long. I really appreciate the opportunity to still be out there playing and performing and doing what I do."
Bryant, 36, entered Sunday's 100-94 win eight points shy of Jordan's mark. He finished with 26 points on 7-of-20 shooting to go along with six rebounds and two assists. Bryant now trails only Abdul-Jabbar (38,387) and Malone (36,928) in career NBA points.
For Bryant, the milestone is no small feat, as he forged his Hall of Fame career in Jordan's shadow, with every achievement measured against his idol, almost since the day Bryant entered the league in 1996 at the age of 18.
"I congratulate Kobe on reaching this milestone," Jordan told the Associated Press in a statement. "He's obviously a great player, with a strong work ethic and has an equally strong passion for the game of basketball. I've enjoyed watching his game evolve over the years, and I look forward to seeing what he accomplishes next."
"He knows how much I've learned from him," Bryant said of Jordan. "From the other legends, but him in particular."
Phil Jackson coached both players in the NBA. he won six titles with Jordan's Bulls and five with Bryant's Lakers, and he wrote in his book "Eleven Rings" that Bryant was "hell-bent on surpassing Jordan as the greatest player in the game."
Bryant disputes Jackson's claim and has downplayed topping Jordan's scoring total for weeks. "It's really not a big deal to say I passed him for something like that," Bryant said. "It's a great accomplishment, but the true beauty is in the journey."
To commemorate the achievement, Nike, which sponsors both athletes, put a special edition "Mamba Moment" shoe on sale online for $245.
LeBron James, who grew up admiring Bryant, was one of many who took to Twitter to congratulate the future Hall of Famer.
Lakers great Magic Johnson also checked in via Twitter to praise Bryant.
Information from ESPN.com's Dave McMenamin, ESPN.com's Darren Rovell and The Associated Press contributed to this report.