Tony Parker had 20 points and nine assists, Kawhi Leonard added 18 and the Spurs wasted little time sending a message to the visiting Grizzlies who are experiencing their first conference finals.
San Antonio, meanwhile, is trying to get back to the NBA finals for the first time since 2007 and looked especially determined in Game One of the best-of-seven series.
Game Two is on Tuesday in San Antonio.
Having been inactive since Wednesday when they finished off the Oklahoma City Thunder in the second round, Memphis came out slow and fell behind by 17 after the first quarter.
The Grizzlies briefly pulled within 62-56 late in the third, but San Antonio spread the floor and hurt Memphis with 14 three-pointers and 28 assists for the game.
Quincy Pondexter led Memphis with 17 points off the bench while Marc Gasol added 15. Zach Randolph had his worst game of the playoffs, managing just two points on 1-for-8 shooting.
Danny Green put up 16 for the Spurs who are seeking revenge for their past post-season matchup with the Grizzlies. Memphis stunned San Antonio in the first round of the 2011 playoffs.
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