Bryant set the record by hitting a pair of free throws with 5:24 remaining in the second quarter. Only Hall of Famers Kareem Abdul-Jabbar (38,387 points) and Karl Malone (36,928) sit above Bryant on the scoring list.
"It's a huge honor, it's been such a long journey," Bryant told ESPN in a postgame interview. "It's going by really fast, though. It feels great to be at this point. I try to learn so much from [Jordan] in particular. He's been such a huge part of my success and my career, giving me advice and offering mentorship and things like that. That relationship has meant everything to me."
After Bryant made his second free throw, the game was stopped briefly so that Bryant could exchange hugs and handshakes with members of both teams and receive the game ball from Timberwolves owner Glen Taylor. Bryant also embraced Lakers coach Byron Scott and trainer Gary Vitti before play resumed.
"I congratulate Kobe on reaching this milestone," Jordan said, in a statement obtained by the Associated Press. "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."
Lakers legend Magic Johnson added his congratulations in a series of Twitter messages.
"Congrats to Kobe Bryant on passing his idol Michael Jordan for [third] on the NBA all-time scoring list," Johnson wrote. "Laker fans we've been so blessed to watch Kobe Bryant, one of the top [five or six] best players ever, play in a Lakers uniform! Just like we've never seen another player like Michael Jordan, we will never see another player like Kobe Bryant!"
The 36-year-old Bryant passed Jordan in his 1,269th career game and holds a 25.5 points per game average for his career. Jordan accumulated his total in 1,072 games and retired (for the third and final time) with a 30.1 points per game career average.
"Congrats Bean," James wrote on Twitter, referring to Bryant by his middle name. "#ThirdAllTime #LivingLegend."
Jordan had held the No. 3 spot on the scoring list since Jan. 22, 2003, when he hit a jumper for against the New Orleans Hornets to move past Hall of Fame center Wilt Chamberlain.
Bryant finished with a team-high 26 points, giving him a career total of 32,310 points. Carlos Boozer added 22 points and 13 rebounds off the bench for the Lakers.
Shabazz Muhammad led the Timberwolves with a game-high 28 points and nine rebounds. Andrew Wiggins added 16 points and two rebounds.
The Lakers improved to 8-16 while the Timberwolves dropped to 5-18.