They remained unbeaten in Game 5s, including two previous victories when the series was tied at 2-2. Of the 27 times the finals have been tied at 2-2, the Game 5 winner has won 20 of them.
Miami was the most recent loser, falling to Dallas in Game 5 in 2011 before being eliminated at home the next game.
"We're going to see if we're a better ballclub and if we're better prepared for this moment," Wade said.
San Antonio shot 42 of 70, right at 60 percent. The last team to make 60 percent of its shots in the finals was Orlando, which hit 62.5 in Game 3 against the Lakers in 2009, according to STATS.
"They just absolutely outplayed us," Heat coach Erik Spoelstra said. "At times they were just picking one guy out at a time and going at us mano y mano. That will change."
Ray Allen scored 21 points on the night for the Heat as he watched Green shatter his finals 3-point record. Green has 25 3s in the series. Allen made 22 3-pointers in six games in the 2008 finals for Boston.
Chris Bosh scored 16 points for Miami, Wade had 10 assists, and James had eight assists and six rebounds, but it was their defense that let the Heat down in this one.
The Heat were within one with 3:05 left in the third quarter before Green hit yet another 3-pointer and Ginobili followed with the stretch that turned the game into the fourth straight blowout of the finals.
The crafty lefty plays with a flair developed on the courts of Argentina and perfected in Europe before coming to the NBA. He sees angles other players can't and takes risks few others would, but his style has been the perfect fit alongside Duncan and Parker.
He converted a three-point play, tossed in a floater with his left hand as he drifted right, and found Tiago Splitter under the hoop with a pass to make it 85-74.
He flipped in another runner with 2.9 seconds to go in the period, sending the Spurs to the fourth with an 87-75 lead as fans chanted "Manu! Manu!" during the break between the third and fourth quarters.
Ginobili had been averaging just 7.5 points on 34.5 percent shooting in the series, making only three of his 16 3-point attempts. But Popovich made the finals' second lineup change in two games, after the Heat inserted Mike Miller to start Game 4.
Ginobili didn't make a start this season and certainly hadn't been playing like someone who belonged with the first five. But in the Spurs' biggest game of the season, they remained confident he would break out, and they were right.
"I knew that I was not scoring much and I felt it in the air. But I tried not to care about it. I know I'm critical enough of myself to be worrying about what other people say," Ginobili said.
It was the first time he scored 24 or more points since having 34 on June 4, 2012, against Oklahoma City, according to STATS.
The AT&T Center crowd roared when Ginobili was the last starter announced, the cheers growing louder when he made a jumper — originally ruled a 3-pointer but later overturned by replay — on the first possession. He assisted on the Spurs' next three baskets, and it was 15-10 when he later hit a 3 that did count.
Parker picked it up from there, dancing his way into the lane repeatedly and scoring seven points in a 12-0 run that made it 29-17.
Leonard's 3-pointer with 4.7 seconds left, on an assist from Ginobili, made it 32-19 and gave the Spurs 12 makes in 19 attempts (63 percent) in the opening 12 minutes.