Jayson Tatum scored 22 points and Jaylen Brown contributed 27 in a strong all-around display from Boston, with all five starters in double figures as the Celtics won their home opener, a rematch of last year's Eastern Conference championship series.
Miami trailed by just three points with 47.1 seconds left when Jimmy Butler was called for a foul on White, which was unsuccessfully challenged by furious Miami coach Erik Spoelstra.
White then drained his two free throws and when Tyler Herro missed a 3-point jumper and Brown sank his from 30-feet out, Miami's resistance was finally over.
Three crucial blocks added to an impressive performance from White, who was delighted with beating a Heat team that secured a place in the NBA Finals with a game-seven triumph at Boston. "Anytime you're on home court, you want to protect the home court and obviously, last time we played them here, they came out winning," White said. "It's always a big game every time we play against them and we're going to see them down the line a lot of times.