The Spurs played their motion offense to near perfection in the first half leading by as many as 25 points despite the best efforts of Miami's LeBron James and took a massive 71-50 lead into intermission.
San Antonio survived a third-quarter comeback that brought Miami within seven points at 81-74 late in the third quarter, but the visitors reasserted themselves to win going away for a comfortable win that ended the Heat's 8-0 perfection at home this postseason.
Four-time NBA most valuable player James scored 22 points to share Miami scoring honors with Dwyane Wade, although James was never able to take control of the game.
James scored 14 points in the first quarter with the next highest scoring Heat player Ray Allen getting three as the Spurs charged out to a 41-25 lead.
James scored only eight points the rest of the way.
"They came out in a different gear than we were playing at," said a frustrated Erik Spoelstra, coach of the two-time defending NBA champion Heat.
San Antonio put on an offensive clinic in the opening half combined with remarkable shooting accuracy.
The Spurs hit 25 of 33 shots for a 75.8 percent shooting percentage that was an NBA Finals record for a half.
San Antonio also applied their high energy pressure on the defensive end, taking advantage of some sloppy play by the Heat to create 20 turnovers, including seven committed by James.
Game Four of the National Basketball Association championship series will be played on Thursday on the Miami Heat's home court.
(Reporting by Larry Fine in New York; Editing by Gene Cherry)