"I don't think we'll ever shoot 76 percent in a half ever again," Spurs coach Gregg Popovich said.
The Spurs led by as much as 25 and were only briefly challenged in their second lopsided victory in the series.
Unlike Game 1, when they didn't pull away until the final minutes, the Spurs were up big before halftime in this one.
Returning to the arena where they were oh-so-close to winning a fifth championship last year, the Spurs came out playing like they were trying to build a lead that was impossible to blow.
They shot 13 of 15 and led 41-25 lead after the first quarter, then hit their first six shots of the second in front of a stunned crowd in Miami to go ahead 55-30.
Leonard scored only 18 points in the first two games, looking frustrated while getting into foul trouble trying to defend James in Game 2. But he had his outside shot working early and the effect on the Spurs' offense was obvious. He made his first six shots and finished 10 of 13 from the field.
LeBron James and Dwyane Wade had 22 points for the Heat, who host Game 4 on Thursday.
The last three NBA seasons ended in this building, the last two followed by Heat championship parades.
The Spurs nearly canceled the last one, building a five-point lead in the final half-minute of regulation of Game 6, a title seeming so certain that workers were already making preparations around the court.
But the Heat rallied to win in overtime and took Game 7, leaving the Spurs with a summer to think about the one that got away.
They're in good shape to get another chance.
With the league scrapping the 2-3-2 format for the NBA Finals in which the lower seed played three consecutive home games the Spurs would have a chance to wrap it up in San Antonio on Sunday in Game 5 if they can win Thursday.
Chris Bosh took only four points and scored nine points for the Heat, who for the second straight year will have to overcome a 2-1 finals deficit after being blown out in Game 3.
This rout came on their home floor, where they had been 8-0 this postseason and had won a franchise-record 11 in a row since the Spurs beat them in Game 1 last year.
Manu Ginobili scored 11 for the Spurs, who dropped Game 2 thanks to some mistakes down the stretch, then rebounded with a level of ruthless execution that had never been seen before.
They inserted Boris Diaw into the lineup, countering Miami's small lineup and creating more ball movement that clearly helped Leonard. The game got off to a crisp start, with the Spurs making their first five shots and Miami opening 4 for 4.
Turned out San Antonio was just getting started.
Coach Erik Spoelstra said he would keep communicating with James as he did in Game 2 to make sure there were no lingering problems from the cramps that forced him to miss the final minutes of the opener.
But there was no way he could rest James early because James was the only one keeping the Heat in the game. He had 14 of their first 20 points, but even James couldn't keep up with the Spurs' pace.
The Spurs "came out at a different gear than what we were playing at, and it just seemed we were on our heels the most part of the first half," Spoelstra said. Spurs 111, Heat 92
Miami 19 24 34 21 98
S. Antonio 26 28 20 36 110
SAN ANTONIO (111)
Leonard 10-13 6-7 29, Duncan 4-7 6-8 14, Diaw 3-6 2-4 9, Parker 4-10 6-6 15, Green 7-8 0-1 15, Bonner 0-0 2-2 2, Ginobili 4-8 2-2 11, Mills 2-5 0-0 5, Splitter 2-3 2-2 6, Belinelli 1-3 0-0 3, Baynes 1-1 0-0 2.
Totals 38-64 26-32 111.
L.James 9-14 2-3 22, Lewis 5-7 0-0 14, Bosh 4-4 0-0 9, Chalmers 0-5 2-2 2, Wade 8-12 6-8 22, Andersen 0-1 3-4 3, Allen 3-8 3-3 11, Jones 0-0 0-0 0, Cole 3-9 1-2 8, Douglas 0-1 1-2 1, Haslem 0-1 0-0 0.
Totals 32-62 18-24 92.
3-Point GoalsSan Antonio 9-20 (Leonard 3-6, Belinelli 1-1, Diaw 1-2, Green 1-2, Ginobili 1-3, Mills 1-3, Parker 1-3), Miami 10-21 (Lewis 4-5, Allen 2-4, L.James 2-4, Bosh 1-1, Cole 1-2, Wade 0-1, Douglas 0-1, Chalmers 0-3). Fouled OutNone. ReboundsSan Antonio 37 (Duncan 6), Miami 31 (Andersen, L.James 5). AssistsSan Antonio 21 (Mills, Parker 4), Miami 17 (L.James 7). Total FoulsSan Antonio 25, Miami 26. A19,900 (19,600).