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 the intermission.
San Antonio survived a comeback that brought Miami within seven points at 81-74 late in the third quarter, but the visitors reasserted themselves to secure a comfortable victory that ended the Heat's 8-0 perfection at home this post-season.
Kawhi Leonard, who had averaged nine points a game in the first two contests, led the Spurs with a career high 29 points. Tony Parker and Danny Green both pitched in with 15 points.
"An unbelievable game by Kawhi," Spurs guard Manu Ginobli said. "He was sharp. He was attentive and he had a great game on both ends of the floor."
Four-time NBA most valuable player James scored 22 points to share Miami scoring honours with Dwyane Wade, although James was never able to take control of the game.
He 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," Heat coach Erik Spoelstra said.
"It just seemed that we were on our heels the most part of the first half. And then when we started to get to a different gear in the third quarter, it was just hard to change the energy of the game."
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.
"We were just kind of pushing the ball and things were working for us and we were kind of going with the flow," Spurs forward Tim Duncan said.
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.
"It's a long series," Spoelstra said. "We have to be able to manage this. We have to go through the process together and somehow collectively come out with a much better response on Thursday."
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