Tim Duncan had 20 points, 14 rebounds and three blocks, and Manu Ginobili scored 13 points for the Spurs, who are in the finals for the first time since 2007 and are pursuing their fifth championship.
LeBron James had 18 points, 18 rebounds and 10 assists for his 10th career playoff triple-double and Dwyane Wade scored 17 for the defending champion Heat. But James made just 7 of 16 shots, missing his last shot in the final 5 seconds, and managed his lowest scoring output of the playoffs.
Kawhi Leonard deserves most of the credit for that, with the 6-foot-7 wing player hounding James on the perimeter all night long and not backing down.
Game 2 is Sunday night in Miami.
These Spurs were supposed to be rusty after a nine-day layoff and Duncan showed some signs of that early with an 0-for-5 start. But once those 37-year-old bones got going, the Spurs showed that this will series will be anything but a coronation for King James.
The Spurs trailed for most of the first three quarters, but Duncan kept the Heat from running away by controlling the paint and moving the ball. Parker's two free throws gave San Antonio a 77-76 lead in the fourth quarter and Duncan's putback pushed the lead to 83-79 with 5:30 to go.
James scored on two straight Miami possessions and Ray Allen hit three free throws to make it 88-86 Spurs with 1:28 to go.
Duncan hit two free throws and Chris Bosh missed an open 3-pointer on the other end and Parker finished off the Heat with a shot clock-beating, leaner after falling to his knees, just in front of James that gave the Spurs their final margin of victory.
Leonard had 10 points and 10 rebounds in a remarkable NBA Finals debut.
Unlike Indiana, which had several big, strong perimeter defenders to throw at James in their seven-game Eastern Conference finals clash, the Spurs entered the season relying on Leonard to get the job done.
Leonard picked up two quick fouls, as did Duncan, while trying to deal with the MVP's aggressive attacks on the rim. But he didn't commit another one for the rest of the game.
Bosh finished with 13 points and the big man was 0 for 4 from 3-point range and Wade was held scoreless in the fourth quarter after a vintage first 36 minutes.
The much-hyped matchup of past vs. present was every bit the air-tight, back-and-forth affair most expected. Each time Wade and the Heat appeared to be taking control in the first 36 minutes, Duncan and the Spurs clamped down on defense, got a quick bucket on the other end and halted the Miami burst.
Bosh's spinning layup gave the Heat a seven-point lead early in the third quarter, but the Spurs fired right back with a 6-0 surge to keep it close.
Everyone expected James to take charge right away in this series, just as he has for the last two years. His triple-double -- 26 points, 13 assists and 11 rebounds -- clinched his first title in Game 5 against Oklahoma City last year, and he reached that plateau again early in the fourth quarter.
But the scoring wasn't there like it has been all playoffs, and when Wade disappeared in the fourth, the Heat were in big trouble.
After a quiet start, Wade asserted himself in the second quarter, showing plenty of spring in his step while barreling toward the rim like the Wade of old. He scored six straight points midway through the second quarter when James went to the bench, giving the Heat a 44-38 lead.
But the Spurs got a throwback performance of their own from the 37-year-old Duncan, who hit a 20-foot jumper just before the first half buzzer sounded to keep the game every bit as tight as this entire series is expected to be.
James bulled to the bucket in transition to score on a layup, then fed Norris Cole for Miami's sixth 3-pointer of the first half for a 38-29 lead before hitting the bench for the first time.
The Spurs swept Memphis in the Western Conference finals to give banged up veterans Manu Ginobili, Parker and Duncan some much-needed recovery time while the Heat suffered through a rugged seven-game series against the Indiana Pacers.
The last time the Spurs were here, they won their fourth title by beating the Cleveland Cavaliers and a young LeBron James in 2007. Now Duncan, Parker and Ginobili are on one last ride, one final push. And again, James stands in their way.
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