In a rematch of last year's Western Conference finals, the Spurs shot 52 percent from the field and made 11-of-20 from 3-point range to begin their season.
San Antonio is trying to bounce back from a devastating seven-game loss to Miami in last year's championship series, one the Spurs appeared to have wrapped up in Game 6 before a dramatic 3-pointer from Ray Allen with five seconds remaining kept the Heat alive.
Veteran San Antonio center Tim Duncan left the game with a chest contusion, having played just 17 minutes. The team had no immediate word as to the seriousness of the injury.
The Spurs took charge by outscoring Memphis 30-7 in the second period. Tony Allen led the Grizzlies with 15 points.