San Antonio had a two-point lead with 3:30 to play thanks to a 3-pointer by Gary Neal but the Spurs did not score another point after that.
Minnesota won its second straight meeting with the Spurs after having lost to San Antonio 16 straight times. The Timberwolves have defeated the Spurs just three times in their last 24 confrontations.
Love scored 18 points and had 16 rebounds for his 17th straight double-double. Rubio had 18 points and 10 assists.
Tony Parker scored 20 for the Spurs, who had captured two in a row.
Minnesota, which won just 17 games last season and 15 the season before that, has nine victories this year and is only one game below .500.