The Timberwolves held a two-point lead with 7:42 to play, but the Spurs dominated the rest of the way to win on the road for the 17th time this season -- most in the NBA.
Parker went 9-of-9 from the foul line and scored 31 points while Danny Green added 28. It was San Antonio's 11th straight victory and brought them within one of becoming the first team in the league this year with 40 wins.
San Antonio played without center Tim Duncan, who is suffering from sore knees and ankles.
Nikola Pekovic had 21 points and 10 rebounds for the Timberwolves, who have won only twice in the last 15 games.
Notable deaths of 2014 [PHOTOS]