The Heat, which recovered from a 10-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 became the first tenth-seed to reach the NBA playoffs via the play-in, and they did so via two wins on the road, having also won in Chicago on Wednesday.
In Atlanta, 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.
The final spot in the Western Conference playoffs was secured by the Memphis Grizzlies, which beat the Dallas Mavericks 120-106.
Despite dealing with an ankle problem, Ja Morant scored 22 points and made nine assists for the Grizzlies, who will face the first-seeded Oklahoma City Thunder in the first round.
For Dallas, the defeat concludes a miserable season which included the departure of star Luka Doncic to the Los Angeles Lakers.
Anthony Davis, who moved to Dallas in that controversial trade, received medical treatment for injury problems throughout the game but led the team with 40 points and nine rebounds.
Memphis led by 15 points at the end of the first quarter, and although Dallas fought back in the third, they never truly threatened the Grizzlies.
Morant indicated that the painkillers had worked for his sprained ankle.
“I couldn’t feel it. That’s why I was out there,” he told ESPN.
“(We are) the underdogs. Obviously, we go on to face a tough team in OKC, but we have all the confidence in ourselves and (are) ready to go on Sunday.
“It’s a big challenge. Obviously, you know, we all have seen them, you know, over this season. Very well-rounded team. We have to be very sound defensively. Very disciplined and just play our type of basketball,” he added. (AFP)
