The 20-year-old netted 22 in game three before coming off the bench to great effect on Wednesday, punishing the Celtics for their 19 turnovers through the game with 17 points in the final quarter alone.
His contribution broke Dwayne Wade's post-season Heat rookie record of 27.
The Celtics nearly hit back as they pulled within three with 16 seconds on the clock. The Heat's Jimmy Butler gave Boston a sniff when he missed a shot with 1.1 seconds left, but the Celtics were without a timeout and could not manage a shot.
Boston, for whom Jayson Tatum scored 28 points, go into Saturday's game five needing a win to keep their season alive.