Led by Bam Adebayo and Duncan Robinson with 22 points each, Miami won 129-121 to move into a tie for fifth place in the Eastern Conference, securing a post-season spot.
Boston have now lost seven of 10 and will have to seek a play-off position through the play-in tournament, featuring teams seven through 10 in each conference.
Kevin Durant had 21 points and eight assists to help the Brooklyn Nets to a 115-107 win at the Chicago Bulls.
Joe Harris had 17 points and Bruce Brown 15 as the Nets, second in the Eastern Conference, won a second straight game to boost their run to the play-offs after losing four in a row.
Zach LeVine had 41 points for Chicago, but the Bulls’ post-season hopes look forlorn after the end of their three-game winning streak.
The Los Angeles Clippers beat the Toronto Raptors 115-96 in Tampa in a confidence boost for the play-offs.
Kawhi Leonard scored 20 points and Paul George had 16 in an all-the-way win for the Clippers, who stayed one game ahead of the Denver Nuggets in the race for third place in the West, with both teams having three road games left before the play-offs.
Chris Boucher had 16 points and seven rebounds for the Raptors, who lost their seventh game in eight and are out of post-season contention in 12th spot.
In other games, the Minnesota Timberwolves won 119-100 at the Detroit Pistons, the Denver Nuggets recorded a 117-112 victroy at the Charlotte Hornets, and the Memphis Grizzlies overcame the Dallas Mavericks 133-104,
The Indiana Pacers beat the visiting Philadelphia 76ers 103-94, the Milwaukee Bucks won at home against the Orlando Magic by 114-102, the Golden State Warriors saw off Phoenix Suns 122-116, the Sacramento Kings got the better of the Oklahoma City Thunder 122-106, and the Los Angeles Lakers scored a thrilling 101-99 win over the visiting New York Knicks in overtime.