Trailing by eight with 2:50 left, Miami went on a 9-0 run and took a 99-98 lead on center Hassan Whiteside's layup with 58 seconds left.
Damion Lee attempted a driving short jumper in the lane with just over one second left, but Richardson blocked the shot. After two free throws by Richardson, the guard then blocked a 3-pointer by Atlanta's John Collins at the buzzer.
Goran Dragic scored 22 points and grabbed 10 rebounds for Miami, and Whiteside had 18 points and 12 boards.
The spot in the postseason was the 18th in the last 23 seasons for the Heat and 20th overall in 30 campaigns.
The win in the final contest of the Heat's four-game homestand also kept them in the seventh seed ahead of the Milwaukee Bucks in the Eastern Conference playoff race. The Heat hold the tiebreaker over Milwaukee, having beaten the Bucks 3-0 in the season series.
Collins led Atlanta with 19 points, and Tyler Dorsey had 18. Lee added 16.
The Hawks dropped to 6-33 away from home, matching the Memphis Grizzlies for the NBA's lowest total for victories on the road.
The Hawks led early in the first quarter behind five points from Prince, but the Heat dominated play in the paint, piling up a 16-4 advantage through eight minutes as they led 20-18.
Whiteside had nine points, six rebounds and three blocks in 11 minutes as Miami shot 50 percent and held a 30-25 lead after the first quarter.
Lee helped Atlanta regain the lead in the second, scoring 10 of his 12 first-half points, as the Hawks outscored Miami 31-22 to take a 56-52 halftime lead.
Miami charged back in the third with a 9-0 run, punctuated by a Dragic trey, to take a 69-61 lead in the third quarter. However, Dorsey and Collins hit threes for Atlanta in the final minute of the third quarter to tie the game at 78-all.
--Field Level Media
Atlanta | Miami | |
John Collins 19 | Scoring | Goran Dragic 22 |
Isaiah Taylor 9 | Assists | James Johnson 6 |
John Collins 10 | Rebounds | Hassan Whiteside 12 |
Damion Lee 3 | Free Throws Made | Hassan Whiteside 4 |
Damion Lee 3 | Steals | Goran Dragic 3 |
John Collins 1 | Blocks | Hassan Whiteside 3 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Atlanta | 98 | 42.0 | 13-33 | 11-15 | 24 | 49 | 1 | 10 | 18 |
Miami | 101 | 45.1 | 8-33 | 11-13 | 22 | 46 | 8 | 10 | 14 |