The Timberwolves wiped out a 10-point deficit to tie the score at 94-94 with 1:22 left before Bryant converted a long three-point shot over two defenders. He then scored his 26th point of the night 42 seconds later with a free throw.
Nick Young (seven points) finished the scoring for the night with a pair of free throws, giving the Lakers their six-point winning margin.
Carlos Boozer added a double-double (22 points, 13 rebounds) off the bench with 22 points and 13 and Wesley Johnson contributed 12 points and six assists for the Lakers, who shot 42% from the field and 29.4% (5 of 17) from three-point range.
Minnesota was led by UCLA product Shabazz Muhammad, who scored 28 points off the bench in 27 1/2 minutes. Zach LaVine, also of UCLA, started in place of point guard Mo Williams (back), giving the Timberwolves 10 points and six assists.
The Timberwolves shot 42.2% from the field and 30% (3 of 10) from behind the arc.
The Lakers (8-16) will try to win their fourth straight on Monday when they play the Pacers (7-17) in Indianapolis. The Timberwolves (5-18) are off until Tuesday, when they'll play the Wizards (17-6) in Washington.
The Lakers pulled ahead by 10 points with about 5 1/2 minutes left in the third quarter but couldn't hold the double-digit lead heading into the fourth.
The game was paused to honor Bryant, with Timberwolves owner Glen Taylor handing the game ball to the Lakers all-star, as players on both teams took a moment to congratulate Bryant.
Bryant finished with 14 points in the half on three-of-10 shooting, but he went seven for seven at the free-throw line.
The Lakers shot 42.9% from the field as a team. Carlos Boozer added eight points and six rebounds off the bench.
Bryant missed four of five shots, scoring four points, four shy of Jordan's 32,292 points.
The Lakers were led by Wesley Johnson with six points as the team shot 40.9% from the field.
The Wolves shot 42.1%, with rookie Andrew Wiggins leading the way with six.
The Lakers (7-16) look to win their third in a row, visiting the Minnesota Timberwolves (5-17) on Sunday.
The same players are out Sunday and Mo Williams has been sidelined recently with back spasms.
For an in-depth breakdown, check out Preview: Lakers at Minnesota Timberwolves.