Dario Saric tallied 20 points and Ersan Ilyasova had 17 points and 14 rebounds for the 76ers, who have won 17 straight games dating back to March 13.
Forward Ben Simmons narrowly missed a triple-double in his first playoff game by piling up 17 points, 14 assists and nine rebounds for Philadelphia, which played without star center Joel Embiid (orbital fracture).
The 76ers were 18 of 28 from 3-point range. Redick, Belinelli and Saric each made four 3-pointers apiece and Ilyasova knocked down three.
Kelly Olynyk scored 26 points off the bench for the Heat. Goran Dragic tallied 15 points, James Johnson had 13 and Dwyane Wade added 11 for Miami, which committed 18 turnovers while shooting 44.9 percent from the field.
Game 2 is Monday in Philadelphia.
The 76ers, who shot 47.4 percent from the field, were playing in their first playoff game since 2012 but looked more ready for the stage than a Miami franchise that is part of the postseason for the eighth time in coach Erik Spoelstra's 10 seasons. The Sixers outscored the Heat 74-43 in a dominant second half effort.
Philadelphia used a 34-18 third quarter burst to turn a four-point halftime deficit into a 90-78 lead. The Heat were just 5-of-19 shooting in the quarter.
Dragic hit a 3-pointer to start the scoring in the third before the 76ers rattled off the next 15 points, with Redick's jumper giving Philadelphia a 71-63 advantage with 7:05 remaining. Ilyasova buried a 3-pointer to make it 79-66 with 4:30 left before the 76ers took the 12-point lead into the final quarter.
Redick's 3-pointer in the opening minute of the fourth quarter gave Philadelphia a 96-80 lead. Saric later drained two 3-pointers and Redick hit one during a 12-0 push to increase the advantage to 112-87 with 6:25 left, and the 76ers cruised to the finish with a 40-point fourth quarter.
Olynyk had 14 points as the Heat held a 60-56 halftime lead.
Miami went on a 23-4 burst in the opening quarter to turn a seven-point deficit into a 35-23 lead.
The 76ers scored the final six points of the first quarter as part of an 18-3 surge that saw them take a 41-38 advantage with 8:14 left in the half. The Heat recovered to take a four-point halftime lead.
--Field Level Media
Miami | Philadelphia | |
Kelly Olynyk 26 | Scoring | JJ Redick 28 |
Justise Winslow 5 | Assists | Ben Simmons 14 |
Kelly Olynyk 7 | Rebounds | Ersan Ilyasova 14 |
Goran Dragic 4 | Free Throws Made | JJ Redick 8 |
Josh Richardson 2 | Steals | Marco Belinelli 3 |
Hassan Whiteside 2 | Blocks | Robert Covington 3 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Miami | 103 | 45.5 | 12-26 | 21-31 | 25 | 41 | 6 | 4 | 18 |
Philadelphia | 130 | 47.4 | 18-28 | 22-29 | 34 | 50 | 4 | 9 | 11 |