San Antonio won its third straight to move into fifth in the Western Conference five days after dropping to 10th and out of playoff position.
Karl-Anthony Towns had 23 points and nine rebounds for Minnesota, which dropped to sixth in the West.
The Spurs had lost three straight and nine of 11 but are now unbeaten halfway through a six-game homestand.
San Antonio shot 84 percent in the second quarter, their best shooting quarter since 2010.
Two nights after battling New Orleans’ Anthony Davis on both ends, Aldridge had to take on another All-Star in Towns. Aldridge responded by leading the Spurs in scoring for the 49th time this season while helping keep Towns in check.
Aldridge scored 18 of 21 points during a five-minute stretch in the second quarter, including 12 straight. He capped the run by coming from the weak side to swat Towns’ floater deep into the seats.
Minnesota started quickly, shooting 78 percent from the floor in the first 5 1/2 minutes while San Antonio floundered at 17 percent. Spurs coach Gregg Popovich called timeout, only to watch the Timberwolves’ Jeff Teague steal the ball once play resumed.
Andrew Wiggins scored 21 points for Minnesota and Teague had 16.