In April in the NCAA championship game, Chalmers hit a last-second 3-pointer that forced overtime as Kansas rallied to beat Memphis.
"Actually, it made my heart jump, thinking what happened last year," Chalmers said. "It was a great experience."
Michael Beasley scored 19 points for Miami (2-5). Udonis Haslem added 18 on 8-of-10 shooting, and Daequan Cook had 17 points. Chalmers, 3-for-3 from 3-point range, had 11 points. Tony Parker led San Antonio (3-4) with 16 points.
Chalmers hit his winning 3-pointer after the Spurs' Roger Mason tied it on a driving layup with 10 seconds left.
"I guess we have to tell him every place we go that it's San Antonio," Miami coach Erik Spoelstra said. "He seems to be a guy who rises to the occasion. He certainly stepped up tonight."
Chalmers scored all 11 of his points in the fourth quarter.
"He's pretty special in this town," Spurs assistant coach Mike Budenholzer said. "Maybe next time we can put more pressure on him."
The Spurs (3-4) will open the regular season Wednesday night at home against Phoenix. The Heat will open at New York, also Wednesday night.
Miami star Dwyane Wade did not play.