The Heat, who recovered from a ten-game losing streak in March to reach the play-in, will now face the top-seeded Cleveland Cavaliers in the opening round of the playoffs.
Miami become the first tenth-seed to reach the NBA playoffs via the play-in and they did so via two wins on the road having won in Chicago on Wednesday.
Miami dominated the opening half, leading by 17 points before going in 62-53 up at the interval but the Hawks fought back superbly, taking the lead 91-88 with 7:36 left.
Atlanta then opened up a 98-92 advantage before Miami came back again only for Trae Young to level the game with 1.1 seconds remaining after a driving lay-up.
But the Heat saved their best for last with Davion Mitchell making three three-pointers in overtime and Herro adding two more.
"Two competitive teams, fighting for the last spot in the playoffs. That was exactly what you saw. Both teams were deserving. I loved how my team fought," said Herro.
"Every single run that they made, we answered. And I feel like this entire season has really built us up for this point.
The Cavaliers will start as heavy favourites in the best-of-seven series which gets underway in Cleveland on Sunday.
Young top-scored for Atlanta with 29 points while Onyeka Okongwu scored 28 and grabbed 12 rebounds.