San Antonio got 67 points from its bench, including 17 from Davis Bertans and 15 points from Danny Green. The Spurs ended a two-game losing streak but won for just the second time in eight games.
Parker scored four straight baskets over a two-minute stretch midway through the fourth quarter that turned a game tied at 85 into a 93-87 San Antonio lead with 4:01 to play.
Kyle Anderson, with 11 points, was the only Spurs starter in double figures. LaMarcus Aldridge returned to the lineup for San Antonio after missing a game and a half with a sprained right ankle and was largely ineffective, scoring seven points and grabbing eight rebounds in more than 31 minutes of court time.
Marc Gasol led the Grizzlies with 23 points and took 10 rebounds. Dillon Brooks added 21 points, JaMychal Green scored 14 points and grabbed 15 rebounds and Kobi Simmons hit for 13 points for Memphis.
Memphis, who owns the NBA's worst record, has lost 14 games in a row and 12 straight contests on the road, dating back to December. But the Grizzlies did not go down without a real fight.
The Grizzlies led 23-21 after one quarter and began the second period with an 8-2 run that pushed their lead to 31-23. San Antonio answered back, behind Parker's 13 points and Green's eight off the bench and clawed to a 47-45 lead at intermission.
Marc Gasol, who was listed as out of the game in Memphis' pregame injury report, instead started and led all scorers with 13 points in the first half.
The Grizzlies took a 72-70 lead going into the fourth quarter as four Memphis starters were already in double figures after 36 minutes of play.
Next up for the Spurs is Thursday's contest at Golden State, the first of three straight games on the road against powerhouse teams of the Western Conference. The road trip will also take San Antonio to Oklahoma City and Houston.
Memphis will try to break its extended losing streak at Chicago on Wednesday.
--Field Level Media
Memphis | San Antonio | |
Marc Gasol 23 | Scoring | Tony Parker 23 |
JaMychal Green 5 | Assists | Kyle Anderson 4 |
JaMychal Green 15 | Rebounds | LaMarcus Aldridge 8 |
Marc Gasol 4 | Free Throws Made | Davis Bertans 6 |
Myke Henry 4 | Steals | Kyle Anderson 5 |
JaMychal Green 2 | Blocks | Pau Gasol 2 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Memphis | 98 | 52.5 | 8-22 | 6-9 | 26 | 42 | 5 | 8 | 20 |
San Antonio | 100 | 46.1 | 6-22 | 24-31 | 18 | 36 | 4 | 14 | 12 |