The defeat dropped the Grizzlies to 50-24 and into second place in the Southwest division, one loss behind the Houston Rockets.
San Antonio won for the sixth time in seven games, improving to 47-26, sixth in the Western Conference and only three back of Houston with nine games to play in the regular season.
French guard Tony Parker added 17 points, 15 in the second half, while Tiago Splitter had 15 points and eight rebounds for the Spurs, who never trailed.
Zach Randolph led Memphis with 20 points and 13 rebounds while Jeff Green came off the bench to contribute 19 points and Marc Gasol scored 16 points for the Grizzlies.
Mike Conley struggled, producing only six points on 2-of-11 shooting.
The Grizzlies were down 70-66 entering the fourth quarter but San Antonio shot 72.2 percent in the final 12 minutes, Leonard leading the way in keeping the Grizzlies at bay. – Agence France-Presse