Dejounte Murray added 18 points for the Hawks, who avenged a five-game Round 1 loss to Miami last season and earned a matchup with Boston that will start Saturday.
Kyle Lowry scored 33 points — his highest-scoring game in his two Miami seasons — for the Heat, who will host either Toronto or Chicago on Friday to decide the No. 8 seed and a spot against top overall seed Milwaukee in Round 1. The Raptors and Bulls play Wednesday; the winner of Friday’s game opens the series against the Bucks on Sunday.
Tyler Herro scored 26 for Miami, and Jimmy Butler finished with 21.
For the Hawks, four reserves — Saddiq Bey, Bogdan Bogdanovic, Onyeka Okongwu and Jalen Johnson — combined for 53 points.
The Hawks improved to 3-0 in play-in tournament games; that’s the best mark in the NBA, one that New Orleans can match when it plays host to Oklahoma City on Wednesday night.
And they earned this one on the boards. Atlanta outrebounded Miami 63-39, including 22-6 on the offensive glass that keyed a 26-6 edge in second-chance points.
The Hawks took two timeouts in the first 3:53 of the third quarter, as most of what was a 24-point lead with 2:37 left in the first half got whittled away, and fast.
Miami cut the margin to 15 by halftime, then opened the third quarter on a 16-6 run. Add it all up, and it was a 27-8 run in about seven minutes of play to get the Heat within 71-66.
But the Hawks had an answer then, and every other time the Heat made a run. The Atlanta lead was 13 again going into the fourth, and when Miami was within six midway through the final quarter, the Hawks scored five straight to restore a double-digit edge.