Parker scored a team-high 26 points in front of an adoring crowd that was showering him with "M-V-P" chants as the Spurs rolled to a 3-2 lead in the best-of-seven series.
"It was a physical game. Great game. I was just trying to pace myself better, if I can say that, during the game," Parker, who struggled during the second half of San Antonio's Game Four loss on Thursday, told reporters.
"Or else I'd be out of gas like I did in Game Four, where in the second half I didn't have enough juice and my hamstring was kind of fatigued. In this game I was trying to take my time and it helped."
Ginobli, who had been the target of criticism for his recent lack of production, gave the Spurs a much-needed spark with 24 points and 10 assists for his best game of the Finals as the Spurs closed in on their first NBA title since 2007.
LeBron James and Dwyane Wade each scored 25 points for the top-seeded Heat, who have alternated wins and losses over their last 12 playoff games and head home needing two consecutive wins to retain their title.
Game Six is on Tuesday in Miami.
Ginobli, who was only told before Saturday's practice that he would start Game Five, set the tone early when he opened the scoring with a long-distance two pointer 19 seconds into a game the Spurs never trailed.
He was instrumental during a 12-1 run to close the third quarter that gave the Spurs a 12-point lead, setting off chants of "Ma-nu" from an adoring crowd. The Spurs would go on to stretch that lead to 20 points in the final quarter.
"I was having a tough time scoring, and I needed to feel like the game was coming to me, and I was being able to attack the rim, get to the free-throw line, and make a couple of shots," said Ginobli.
"So it felt great when I heard that. To feel that I really helped the team to get that 20-point lead, it was a much-needed moment in the series. So I'm glad to see it happen.
The rejuvenated Spurs closed out the opening quarter on a wild 15-2 run, capped by a three-pointer from second-year forward Kawhi Leonard, that gave the hosts a 13-point lead and sent the home crowd into a frenzy.
Danny Green went 6-of-10 from behind the arc, including one midway through the second quarter that built San Antonio's lead to 42-26 and forced the Heat to call a timeout.
Miami looked poised to grab their first lead of the game when they raced out after the halftime break with a 8-0 run to pull within two points but, just as they did every time the visitors threatened to take control, the Spurs pulled away.
"Once we got it back to one and we felt that we had weathered the storm, then we missed a couple of shots that we normally are accustomed to making, and then it just snowballed down the hill from there," said Heat coach Erik Spoelstra.
"And we couldn't control it ... and so we just didn't show the mental resolve that we needed to at that point."