Kobe Bryant made four key free throws in 102.
Bryant had 34 points and surpassed 29,000 points for his career for the Lakers, who have won 18 in a row over Minnesota.
"It's a good win for us from the standpoint that I thought we came out, were a little flat, turned the ball over and gave them confidence early, but I thought our guys showed some toughness," Lakers coach Mike Brown said.
Nikola Pekovic had 25 points and 13 rebounds in his return to the lineup for the Timberwolves, who had a three-game winning streak snapped. Rookie Derrick Williams filled in for an injured Kevin Love (back spasms) and ended with 22 points and 10 boards.
"It's tough to play against the Lakers. They have a great team and one of the great players," Pekovic said.
Ricky Rubio tallied 15 points and 10 assists for Minnesota, which also got 15 points from Michael Beasley. Rubio injured his left leg in the final seconds of the game.
Trailing by four, 99-95, Pekovic put home an alley-oop slam with 2:19 to play. After Metta World Peace missed a three-pointer, Luke Ridnour made a shot from beyond the arc to give Minnesota a 100-99 lead with 1:33 to go.
Derek Fisher and World Peace both missed three-pointers on the Lakers' next trip down the court. But LA got the ball back after Rubio missed a floater.
Williams was then called for goaltending on Bynum's nine-foot jumper, giving the Lakers the lead with 34.7 seconds remaining.
But Pekovic's tip-in off a Williams miss put Minnesota back in front with 28.6 ticks left on the clock.
Rubio and Bryant locked knees on the ensuing possession, which resulted in a blocking foul. Rubio held his left knee and needed help making his way to the bench. Bryant made two foul shots to give Los Angeles a 103-102 lead with 16.4 seconds to play.
Gasol blocked Williams' jumper in the lane, leading to two more Bryant free throws. Ridnour's three-pointer was off the mark as time expired.
Minnesota made 12-of-14 free throws in the first quarter and took a 33-21 lead into the second.
The Lakers outscored the Timberwolves by a 28-25 margin in the second to cut the gap to 58-49 at the break.
Bryant's three-pointer to start the third ignited an 8-0 LA spurt. The Lakers kept it close and used a 7-2 flurry at the end of the frame to make it 78-78.
Neither team led by more than three in a tight fourth quarter.
Los Angeles is unbeaten in nine straight meetings at Minnesota. The Timberwolves haven't topped the Lakers since a 117-107 double-overtime victory back on March 6, 2007 at Target Center...Pekovic missed the previous two games with a sore right foot...The Lakers improved to 7-14 as the visitor this season...Minnesota had a five-game home winning streak snapped...Timberwolves guard J.J. Barea (ankle) missed the game...Minnesota recalled guard Malcolm Lee from Sioux Falls (NBADL).