The Celtics became just the fourth team in NBA history to level a best-of-seven playoff series after trailing 3-0.
They will now have a chance on Monday to mark an even more impressive milestone if they can become the first team to win a series after losing the opening three games and earn a place in the final against the Denver Nuggets.
It was a crushing loss for Miami, who were less than a second away from reaching their seventh NBA Final before White’s inspired touch.
The Celtics had led for most of the contest but Miami looked to have grabbed the win and the series when Jimmy Butler was fouled, attempting a three-point shot, by Boston’s Al Horford.
With three seconds left on the clock, Butler, who had been well below-par until he came alive late in the fourth quarter, kept his cool to sink all three free throws and give the Heat a 103-102 lead.
Facing elimination, Marcus Smart’s three-point attempt bounced off the rim, but White was alert and strong to tip the rebound into the bucket, the shot leaving his fingertips only a fraction of a second before the buzzer.
The Miami crowd were distraught as the Celtics celebrated in a huddle on the court.
“Ball came to me, I made the shot. That’s what I saw,” said White, reflecting on the game-winning moment.
“It felt good. Everybody was asking me, ‘did you get it off?’ And I was like, ‘yeah, I think so,’ but it was so close, you never know,” he said.
“I’m happy we won. Whatever it takes. We got our backs against the wall. Just happy we won.”
Heat coach Erik Spoelstra rued his team’s luck on the decisive final play.
“That thing just bounced a different way. That’s the only place it could have bounced to hurt us. I thought we had a lot of things covered on that play and sometimes things just don’t break your way,” he said.
Jayson Tatum led Boston with 31 points and had 11 rebounds and five assists, while Jaylen Brown came up with 26 points and 10 rebounds.
Butler went into the fourth quarter with just nine points but ended with 24, while Caleb Martin provided 21 points for Miami.
Butler shot just 5-of-21 and took responsibility for Miami’s situation.
“I told the guys in the locker room, if I play better we are not even in this position,” said Butler, who vowed to be back to his best in game seven.
‘To hell and back’
The Celtics had led by 11 points midway through the second quarter as Miami struggled at both ends of the court, but the Heat rallied to reduce the deficit to 57-53 at half-time.
Boston opened up another double-figure lead in the third, but once more couldn’t quite shrug off Miami, and the Heat found a way to grab the lead with a Butler tip lay-up making it 83-82 with 7:57 left in the fourth.
But the Celtics responded strongly with a 16-5 run before the late drama began to unfold, with Butler scoring 10 points to give Miami the lead with three seconds to go.
Butler was philosophical in defeat.
“That’s basketball for you. Basketball at its finest. Very, very, very entertaining,” he said.
“We can do it. I know that we will do it. We’ve got to go on the road and win in a very, very, very tough environment. But we are capable of it. So let’s get busy.”
The momentum is clearly with Boston after yet again roaring back from a possible exit.
“It gives you a supreme boost in confidence, man. It doesn’t get too much worse than being down 0-3. We feel like we’ve been to hell and back,” said Brown.
“We feel like we can face any adversity that gets thrown at us in the duration of the game or the duration of the season or in the postseason. It all means nothing if we don’t come out and give our best effort on our home floor on Monday night.”