Cleveland suffered their second overtime defeat in as many days, having lost to the Atlanta Hawks on Sunday.
The Cavs, locked in a duel with the Boston Celtics for the top seed in the East, nevertheless rested stars LeBron James and Kyrie Irving in Miami.
"The most important thing is for us to give those guys a rest," Cavaliers coach Tyronn Lue said. "They have carried the load all season."
Cleveland suffered their second overtime defeat in as many days, having squandered a 26-point fourth-quarter lead in a stunning loss to the Atlanta Hawks on Sunday.
Against the Heat, they took a 91-80 lead into the fourth, but Miami stormed back to force overtime and claim the win.
Tyler Johnson had 24 points and Hassan Whiteside added 23 and 18 rebounds as the Heat snapped a three-game home losing streak.
Deron Williams, starting at point guard in place of Irving, led Cleveland with 35 points. Kevin Love added 25 with 10 rebounds before he fouled out with 34 seconds left in overtime.
With the Celtics beating the Brooklyn Nets 114-105, the defeat dropped the Cavs one game behind Boston for first place in the conference.
James has said he isn't concerned about the top seed, and teammate Kyle Korver said Monday that the Cavs just want to get the post-season underway.
"I think we've shown that when we're focused we're a really good team," Korver said of the Cavs, despite a ragged end to the regular season.
The Celtics, however, are eager to go into the post-season as the top team in the East.
"Trying to finish the season with the number one seed, that means a lot to me, personally, so hopefully we can get that," said Isaiah Thomas, who scored 27 points against the Nets.
For the Heat, the victory means they will be fighting with the Indiana Pacers and Chicago Bulls for the last two playoff spots in the East when the regular season concludes on Wednesday.
The Pacers, with 27 points from Paul George, defeated the Philadelphia 76ers 120-111 on Monday and lie second in the Eastern Conference.
The Bulls crushed the Orlando Magic 122-75 and at 40-41 have the same record as Miami with one game remaining for each.
But Chicago own the tiebreaker, so if they finish with the same record as the Heat, the Bulls will claim the eighth and final playoff spot.
Robin Lopez scored 18 points and Jimmy Butler and Jerian Grant had 17 apiece to pace the Bulls. Nikola Mirotic added 16 points and veteran Dwyane Wade chipped in 13 as Chicago won by their biggest margin of the season.
Heat coach Erik Spoelstra said he didn't try to keep track of what the Bulls and Pacers were doing on Monday.
"Our game was enough," he said. "I don't need the ancillary stress."
In Oakland, Golden State starts Stephen Curry and Kevin Durant were watching from the bench in the fourth quarter as the injury depleted Utah Jazz completed a 105-99 victory that ended the Warriors' 14-game winning streak.
Warriors coach Steve Kerr opted to play safe with his key players, resting Curry, Durant and Draymond Green late while Klay Thompson sat out altogether.
The Warriors are already assured of top seed in the West and home court advantage throughout the playoffs.
For the Jazz, however, the win kept them level for fourth place in the West with the Los Angeles Clippers, who thumped the Houston Rockets 125-96 for a sixth-straight win.
Chris Paul scored 19 points and handed out nine assists and Blake Griffin added 18 points for the Clippers.
The Portland Trail Blazers, headed to a first-round playoff series against the Warriors, stunned the San Antonio Spurs 99-98 on Noah Vonleh's layup as time expired.
All five starters scored in double figures for Portland, starting with Shabazz Napier's career-high 32.