Leonard finished with a career-high 29 points, outscoring Miami's LeBron James (22 points) on the same court where the Spurs endured regrettable failures in Games 6 and 7 of last year's Finals.
Leonard's biggest scoring output since he starred at Riverside King High helped San Antonio win on a night it didn't receive huge games from any of its Big Three of Tony Parker (15 points), Tim Duncan (14) and Manu Ginobili (11).
It also gave the Spurs a 2-1 lead in a series that resumes with Game 4 here Thursday.
“I just was in attack mode, trying to be aggressive early,” said Leonard, who failed to score in double figures in either of the first two games and fouled out in Game 2. “Just knocking down a couple of shots just got me going.”
He knocked down more than a couple. Leonard and Danny Green combined to make their first 12 shots, part of a game-opening run in which the Spurs made 19 of 21 shots and went 11 minutes without a miss.
“That will never happen again,” Coach Gregg Popovich said. “That's crazy.”
The Spurs made a Finals-record 25 of 33 shots (75.8%) on the way to a 71-point first half, and it still almost wasn't enough.
The Heat trailed by as many as 25 points before closing to within seven late in the third quarter. But they couldn't crack single digits in the fourth quarter, fans finally streaming out with 3 minutes 35 seconds left.
“They jumped on us and they were the aggressor tonight and had us on our heels from the beginning,” said James, who made nine of 14 shots but committed seven of his team's 20 turnovers. “This is something that at this point in the season shouldn't happen.”
Dwyane Wade finished with 22 points for the Heat, which had been 11-0 on its home court in the playoffs dating to last year's Game 1 loss in the Finals against the Spurs. More emblematic of their performance was guard Mario Chalmers, who missed all five of his shots and had three turnovers.
Leonard made 10 of 13 shots, including a baseline drive for a dunk early in the fourth quarter that seemed to take some of the fizz out of the Heat comeback. Green finished with 15 points on seven-for-eight shooting.
Popovich made the first starting lineup change of the Finals, inserting forward Boris Diaw into the slot previously taken by Tiago Splitter. The move immediately paid off when Diaw found Duncan inside for a layup on the game's first possession.
That foreshadowed an incredible display of ball movement in which the Spurs shot a Finals-record 86.7% during the first quarter while scoring on 19 of 23 possessions.
Leonard responded in a big way to some verbal prodding and literal poking from Popovich, who wanted his emerging 22-year-old star to play with the same assertiveness he had all season before the Finals.
“He was beating me up right there,” Leonard joked. “He wasn't really saying nothing, he just kept hitting me.”
Leonard contributed to the Spurs' painful Game 6 collapse here a year ago, missing a free throw in the final minute. He admitted that loss continued to drive him toward redemption.
"I mean, that's why we're here again,” Leonard said. “We knew we threw away a game and we're back at it. We're not really thinking about last year. It's a new year and we're trying to get this series.”
Thanks to an unreal shooting night, they're halfway there.