Marco Belinelli, who had averaged 18.8 points over his last five games, scored 25. Dwayne Wade has seven points off the bench.
JJ Redick topped all players in scoring with 28 points, and was one of three Sixers to reach the 20-point plateau.
Their only previous victory in the opening game of a post-season series came in the second round against Philadelphia in 2001. Olynyk and James Johnson, who closed with 13 points, three rebounds and four assists, were leading the charge.
May summons ministers to discuss possible military action in Syria
It is not about regime change", May said in a statement. "They agreed to keep working closely together on the worldwide response".
The Heat jumped out to an early lead and took command at the end of the first quarter, 35-29.
Before the first National Basketball Association playoff game played in Philadelphia in six years got started, the always pleasant Philly faithful greeted the Heat with deafening boos and by shouting "SUCKS!" after each player in Miami's starting lineup was introduced.
Miami led at the half, 60-56.
US Defence analyst says Syrian strikes not enough to deter President Assad
The fact that these deaths did not involve chemical weapons makes them no less tragic for their victims and surviving loved ones. But there was a clear warning that if the Assad regime resorts to chemical weapons again, then further strikes may well follow.
Serge Ibaka had 23 points and 12 rebounds, while Delon Wright scored 11 of his 18 points in the fourth quarter for the east's top seeds. Bellinelli and Ilyasova were vital midseason additions for Philadelphia. Embiid is a first-team All-NBA candidate as well as Defensive Player of the Year candidate.
Embiid was a spectator in Game 1 of the first-round series because of a broken orbital bone around his left eye. He is hopeful that he will be able to return for Game 2. Here he is wearing a mask and ringing a Liberty Bell replica.
The 76ers have won 16 straight, but history has shown that a team's entire body of work is more important than a late-season sample.
Wisconsin US senators respond to Syrian airstrikes
The US was also anxious that the strikes would prompt a confrontation with Syria's biggest military ally: Russian Federation . French Defense Minister Florence Parly said that "with our allies, we ensured that the Russians were warned ahead of time".
However, Simmons was not celebrating the team's win in the best-of-seven series and said his focus was on game two on Monday (Tuesday morning Australian time) in Philadelphia.