Tiago Splitter added 17 points and seven rebounds for the Spurs. Manu Ginobili netted 15 points to go with seven assists and five rebounds as San Antonio halted the Grizzlies' four-game winning streak.
Mike Conley scored 28 points and had four steals, while Zach Randolph had 16 points and 10 rebounds for the Grizzlies. But Memphis lost Marc Gasol to an apparent sprained left knee early in the second quarter.
The Spanish center, last season's NBA Defensive Player of the Year, appeared to hurt his knee under the Spurs basket with 10:24 left in the second quarter. He went to the locker room and the Grizzlies said his injury would be evaluated further on Saturday.
Even without him, the Grizzlies erased a nine-point fourth-quarter deficit to pull within 79-78. But the Spurs responded with an 8-0 scoring run to regain control of the contest.
French point guard Parker, who scored 11 points in the final frame, netted the first six points of the surge and Tim Duncan's basket gave the Spurs an 87-78 lead with 4:37 to play. The Grizzlies didn't threaten again.
The Spurs, who fell to the Miami Heat in last season's NBA finals, have little time to rest before going for their 10th straight win. They host Cleveland on Saturday.