Parker was 13 of 24 from the field in 36 minutes as the Spurs returned from two game road trip.
San Antonio had five other players in double figures with forward Kawhi Leonard getting 19, while guards Manu Ginobili had 20 and Marco Belinelli 12. Forwards Boris Diaw had 12 and Tim Duncan chipped in 12 with 14 rebounds for San Antonio (18-4).
Down by one with less than three minutes to go, the Spurs Big Three came up big down the stretch. Duncan's layup started a 10-2 run that ended with a pair of free throw from Ginobili that secured the game for San Antonio.
Their defense came up strong and held the Timberwolves to two points from the 2:45 mark to the end of the game.
Minnesota, which was down by eight entering the third quarter, outscored San Antonio 35-18. Love had 19 points and seven rebounds and was unstoppable. He connected on five 3-pointers in the third quarter as San Antonio searched for an answer.
San Antonio's bench outscored the Timberwolves' bench 55-12.
NOTES: Spurs C Aron Baynes (left posterior tibialis strain) and C Tiago Splitter (tightness left calf) did not suit up for the game. Both players are listed day to day. ... Minnesota F Kevin Love leads the NBA with 20 double-doubles this season. He has 211 in his career but is well behind Spurs F Tim Duncan, who leads all active players with 770 career double-doubles. ... San Antonio's defense remains a strong component to their success. They are fourth in the league, allowing only 92.8 points per game. ... Minnesota and San Antonio were scheduled to play in Mexico City on Dec. 4, but the game was postponed because the arena became filled with smoke. The game will be rescheduled in Minnesota, but a date has not been announced.