The Pacers have not always been at their best in escaping the first two rounds of the playoffs, but against the defending champion Heat they again looked like the conference's top seeds to start the best-of-seven series.
Paul George scored a team-high 24 points and had seven assists as Indiana had six players in double-figures on their home floor.
"This is a fun matchup - the one we've been waiting for all year," George told reporters. "(We wanted) the chance to battle this team once again. I'm happy we were able to get the win."
The Pacers have been eliminated from the playoffs by Miami the past two seasons, including in last year's Eastern Conference finals that went all seven games.
On Sunday, Indiana scored the game's first seven points and led by 10 at halftime. The advantage swelled to 19 in the second half and the Heat never found their footing.
Dwyane Wade led Miami with 27 points and LeBron James put up 25 and 10 rebounds.
The Heat began the game with a small lineup, featuring James and Shane Battier at the forwards. After halftime, Miami coach Erik Spoelstra started the bigger Udonis Haslem instead of Battier, but the move provided little help.
"They have a very physical front line. It's going to have to be a collective effort," James said. "We'll figure it out in Game Two."
Indiana big men David West and Roy Hibbert each scored 19 points.
The Pacers have had an unsettling last couple of months, stumbling to end the regular season and playing inconsistently during the playoffs.
They needed the full seven games to overcome the eighth seed Atlanta Hawks in the opening round, and were also challenged throughout six games with the underdog Washington Wizards.
Against Miami, though, they found their form and forced the Heat to regroup.
"They drew first blood," Wade said. "This series has so much basketball left. We believe we can figure it out."
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