Indiana and Chicago grabbed the final play-off berths in the Eastern Conference as Boston secured top seeding.
Both the Pacers and the Bulls needed victory in the last round of regular season to deny Miami a post-season place, and achieved that objective with few alarms.
The Heat beat Washington Wizards 110-102 but lost out to the Bulls who own the tiebreaker after both teams finished with a 41-41 record.
Jimmy Butler scored 25 points for the Bulls in a 112-73 win over the Brooklyn Nets, who had the worst record in the NBA.
Paul George provided 32 points and 11 rebounds as the Pacers beat the Atlanta Hawks 104-86 to seal seventh place in the east.
The Celtics were 112-94 winners against the Milwaukee Bucks, who rested a host of starters, and finished two games ahead of Cleveland as the Cavaliers lost 98-83 to the Toronto Raptors, for whom Norman Powell weighed in with 25 points.
In games between sides already out of play-off contention, the Orlando Magic won 113-109 against the Detroit Pistons and the New York Knicks edged the Philadelphia 76ers 114-113.
In the Western Conference, the one unresolved issue going in to the final round was who would enjoy home court advantage between the Utah Jazz and the Los Angeles Clippers as they vied for fourth place.
The Clippers nicked it with their seventh straight win, a 115-95 victory over the Sacramento Kings, which rendered Utah's 101-97 triumph over the San Antonio Spurs meaningless.
Conference winners the Golden State Warriors beat the Los Angeles Lakers 109-94 and the New Orleans Pelicans were 103-100 winners at the Portland Trail Blazers.
James Harden had a 27 points triple-double as the Houston Rockets beat the Minnesota Timberwolves 123-118, the Dallas Mavericks beat the Memphis Grizzlies 100-93 and the Denver Nuggets won 111-105 against the Oklahoma City Thunder.
Match-ups for the first round of the NBA playoffs:
Eastern Conference
Boston (1) v Chicago (8)
Cleveland (2) v Indiana (7)
Toronto (3) v Milwaukee (6)
Washington (4) v Atlanta (5)
Western Conference
Golden State (1) v Portland (8)
San Antonio (2) v Memphis (7)
Houston (3) v Oklahoma City (6)
Los Angeles Clippers (4) v Utah (5)
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