Miami's habit of making a slow start was particularly acute - they trailed 17-4 in the first quarter and were 37-22 behind midway through the second as the Pacers made them pay for some loose turnovers.
Heat coach Erik Spoelstra shuffled his pack however and Miami came out strong in the third quarter though and took the lead for the first time on the night with a LeBron James dunk putting them 52-51 up with 7:36 left in the quarter.
The game turned decisively in Miami's direction when Wade made a superb steal and set up a three-pointer from Ray Allen and put the Heat eight points ahead.
Allen (16 points) had three other three-pointers in the final quarter for the Heat while James made 26 points and Dwyane Wade 23.
While James and Wade top-scored, James was quick to praise the contribution of some of Miami's less heralded players.
Norris Cole brought energy and aggression to defense and was able to provide some penetration on offense while Rashard Lewis provided some valuable work to frustrate the Pacers' offense.
"Those guys off the bench they did it for us, they've got the game ball for sure," said James, who was annoyed with the team's first quarter.
"We started the game with mental turnovers and mental breakdowns.
"We don't want to keep digging holes, we hate the way we played. We have to start the game like we are down 15.
It was Allen's brilliance from the corner, where he provided a reminder of why he is the league's all-time three-point scorer, that proved to be the difference at the end.
"You can ask anybody in that locker room, there are so many years of pain that he caused us (playing for Boston) and it is great to have him on our side," said Spoelstra.
"It is not just the made baskets. It is the spacing, the movements and he gives you another layout to the offense."
The win tied the second largest playoff comeback in the Heat's history - equalling their performance against the Boston Celtics in the 2012 finals.
But Pacers head coach Frank Vogel said there was no question of the defeat harming his team's confidence.
"We are very early into the series. They took care of their business on home court now we have to come out and get Game Four," he said.
Game Four of the best of seven series will take place in Miami on Monday.