Tony Parker scored 20 and Richard Jefferson added 15 points and 10 rebounds for the Spurs, who improved to 13-0 when scoring over 100 points this season.
Manu Ginobili added 16 points and was 13-of-13 from the line, while George Hill supplied 20 points in a reserve role for San Antonio, which began its six-game home stand with a win.
Michael Beasley scored a game-high 28 points and Kevin Love added 25 and 18 rebounds for Minnesota, which has dropped six straight.
Luke Ridnour and Corey Brewer both finished with 14 points in defeat.
Down 86-71 entering the fourth, the Spurs used a 12-3 run in the opening four minutes of the quarter to trim the Minnesota lead to six.
The Timberwolves’ lead fluctuated around six until the final four minutes when San Antonio used two Jefferson free throws and a Hill fastbreak layup to cut the deficit to 97-95. Wanting to stop the surge, Minnesota quickly called a timeout.
The Timberwolves were able to hold off the Spurs until they sank four consecutive free throws inside three minutes — two apiece from Ginobili and Hill — to tie the game at 99.
After both teams missed multiple shots, Ginobili was sent to the line with 1:13 left with a chance to put San Antonio ahead. He converted on both.
Jefferson’s dunk with 47.1 ticks remaining put San Antonio up 103-99 and from there all the Timberwolves could manage was two Love free throws. Ginobili made two more from the charity stripe and Antonio McDyess added a driving layup with eight seconds left to account for the final margin.
The game was tied at 25 after a back-and-forth first quarter.
Beasley and Love both finished the second quarter with eight points as Minnesota held a slim 54-53 lead at the break.
The Spurs took the lead when Tony Parker opened the third with a short jumper and three-point play conversion, and after Minnesota tied the game with two Ridnour free-throws, the teams traded the lead for the next 5 1/2 minutes.
A Ridnour jumper with 2:22 left put Minnesota up 75-68. The shot started a 13-3 run to end the quarter — that included seven points from Brewer. The Timberwolves took an 86-71 lead into the fourth.
The Spurs have won 23 of the last 26 meetings…San Antonio head coach Gregg Popovich was ejected with 1:10 left in the third after collecting consecutive technical fouls…The Spurs scored 23 points on 17 Timberwolves turnovers…Minnesota is now 1-10 on the road this season…Despite the loss, Minnesota controlled the rebounding margin, 59-37.