Tony Parker added 19 points for the Spurs, who can win their fifth championship with a victory at home in Game 5 on Sunday.
LeBron James had 28 points and eight rebounds for the Heat, but Dwyane Wade was just 3 for 13 for 10 points as the Heat were routed at home for the second consecutive game.
The Heat would have to become the first team to overcome a 3-1 deficit in the NBA Finals to win their third consecutive championship.
And the Spurs haven’t as much as lost three consecutive games since January.
The Spurs took control with balance, eight players scoring in the first quarter alone.
They didn’t have anyone besides James reach double-figures in scoring until 7:37 remained, and by then there were streams of Miami fans filing out of the arena, quite possibly for the final time this season, maybe even for the final time in this “Big 3” era.
James came to Miami seeking help to win titles, and that decision got him two rings so far.
The Spurs dominated again in the first half on Thursday, opening a 55-36 lead at the break.
In the first half, the Spurs shot 56 percent and led by as much as 22 points against the Heat, who looked powerless to slow San Antonio’s ball movement.
Not quite as sharp as when they shot a finals-record 75.8 percent in first half Tuesday night, the Spurs were still plenty good enough to open another huge lead before a Miami crowd that was booing the home team in the final minutes of the second quarter.
Parker scored 12 points in the first half while James had nine points for the Heat, while Wade was 1 for 7 for four points.