Gasol was huge for the Lakers in the fourth quarter with the game still in question, scoring seven consecutive points to push the Lakers ahead by six.
Starting at point guard, Xavier Henry also scored 21, dishing four assists while committing only three turnovers.
The Lakers shot 53.8% from the field but the Wolves dominated the offensive glass with 22 to just seven for the home team.
The Lakers, who even their record at 13-13, avenged a 113-90 loss to Minnesota (13-14) on Nov. 10 at Staples, tying the season series at one. They also overtake the Wolves in the standings, climbing to 10th place in the Western Conference.
The Lakers will visit the Golden State Warriors on Saturday night in Oakland.
Minnesota will stay in Los Angeles for the weekend, playing the Clippers on Sunday.
The Lakers reestablished a lead in the third quarter to forge ahead by five entering the final quarter.
Nick Young scored 19 points off the bench to lead the Lakers, who shot 58.9% as a team.
Kevin Love was the game's leading scorer with 25 points. He also has 12 rebounds. Minnesota shot only 38.6% from the field but had 15 offensive rebounds to just three for the Lakers.
Pau Gasol has 12 points, eight rebounds and eight assists as well as five turnovers.
As a team, the Lakers turned the ball over 17 times but the Wolves weren't far behind at 13.
Starting at point guard, Xavier Henry had 17 points with three assists and three turnovers.
Playing without a point guard proved to be difficult for the Lakers in the second quarter.