Bryant had a chance to clinch the victory when he went to the foul line with 3.4 seconds remaining, but he missed his second attempt to leave the Lakers in front by just three.
Ricky Rubio seized the rebound for the Timberwolves and he dashed down court in hopes of getting off a game-tying 3-pointer.
Bryant, however, reached from behind and got a piece of the ball as Rubio let it go. The resulting shot fell well short, leaving the Lakers with their 22nd straight win over Minnesota.
Los Angeles began the evening with a one-game lead over both Utah and Dallas for the eighth and final playoff spot. The Lakers ended a three-game losing streak.
Nikola Pekovic led Minnesota with 19 points and 16 rebounds.