The Lakers moved a full game in front of Utah for the eighth and final playoff spot in the Western Conference. Both teams have three games remaining.
Portland held a 100-98 lead with just under 6 minutes remaining when Los Angeles went on its key spurt. Bryant finished the surge with a pair of free throws and a jumper.
Bryant made 14-of-27 shots from the field and all 18 of his attempts from the foul line. The Lakers shot 58 percent from the field.
Portland, which has lost nine in a row, was led by Damian Lillard with 38 points.