Darrell Arthur came off the bench to score 14 points and Tony Allen contributed 12 for Memphis, which continued its surprising play against the top-seeded Spurs in their Western Conference quarterfinal series.
The Grizzlies, who took control of the game by outscoring San Antonio 30-15 in the third period, got 11 points and nine rebounds from Zach Randolph.
The Spurs got 23 points from Tony Parker but the all-star guard tuned the ball over seven times.
Manu Ginobili added 14 points while Tim Duncan was held to only six for San Antonio.
Memphis will try to close out the first post-season series win in its history Wednesday in Game 5 at San Antonio.