Olynyk, who signed with Miami last summer, led the Heat with 26 points.
Philadelphia will host Miami for Game 2 on Monday at 8 p.m. on TNT.
Richardson and Covington had extremely similar statistical seasons with the only big difference coming in rebounds per game, where Covington edged out Richardson 5.4 to 3.5.
The 76ers responded, led by their 208cm tall Australian point guard who thrived playing his first National Basketball Association post season game.
The Spurs lacked the firepower to match the Warriors, with their All-Star forward Kawhi Leonard mysteriously refusing to play despite overcoming a quadriceps injury and being cleared to play by the team.
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The Heat will need to regroup and in a hurry with Game 2 around the corner on Monday. "They are culturally sound, been there and done that, years of experience making adjustments". Kelly Olynyk poured in 14 points while James Johnson added 13 points and four assists. Game 3 is Thursday in Miami.
The Heat (6) are hoping their centers, Hassan Whiteside and rookie rebounding extraordinaire Bam Adebayo, can take advantage of Embiid's absence.
If Whiteside can shut down the paint and Miami's wing defense can extinguish any hot three-point shooting during Game 1, Miami will have a good chance of upsetting Philadelphia in their first playoff showdown since 2012.
Jrue Holiday scored 21 points, Nikola Mirotic collected 16 points and 11 rebounds, and Rajon Rondo contributed six points, eight rebounds and 17 assists for the sixth-seeded Pelicans.
The 76ers were forced to play without their best player, center Joel Embiid.