James struggled from the field, shooting 8 of 21, and committed seven turnovers but finished with 11 rebounds for the Cavaliers, who remain third in the Eastern Conference, now 1 1/2 games ahead of Miami.
Kyle Korver made one of two free throws with seven seconds remaining to give the Cavaliers the final margin. Miami's James Johnson rebounded Korver's missed free throw and dribbled down the court but couldn't release a game-tying attempt near the paint with James guarding him as time expired.
Jae Crowder's 3-pointer with 1:21 remaining in the fourth quarter gave Cleveland the lead for good at 88-85.
Josh Richardson's layup with 1:00 remaining cut Cleveland's lead to 88-87, and Miami had an opportunity to take the lead after James' missed 3-pointer with 41 seconds left. However, Tyler Johnson's 3-point attempt with 23 seconds left bounced off the rim.
Isaiah Thomas' two free throws with 18 seconds left gave the Cavaliers another three-point advantage. Thomas converted all nine of his free throws and finished with 13 points.
Channing Frye scored 16 points and Crowder finished with 11 points for Cleveland.
The Cavaliers played their first game without Kevin Love. The All-Star forward is expected to miss the next six to eight weeks after he fractured his left hand in Cleveland's 125-114 loss at Detroit on Tuesday.
Goran Dragic scored 18 points and Richardson finished with 15 for the Heat.
Wayne Ellington was held scoreless, as the Cavaliers limited Miami's top 3-point scorer to four shots in 26 minutes.
Miami shot 3 of 28 on 3-point attempts and 14 of 25 on free throws. The Heat also committed 19 turnovers.
Cleveland was 6 of 26 from long range, 29 of 38 at the foul line.
Miami rallied from a 14-point deficit early in the second period with a 25-9 run to end the first half. Dragic scored eight points and Bam Adebayo added five during the surge.
Dragic's two free throws with 39 seconds remaining in the second quarter gave Miami a 50-48 lead at halftime.
--Field Level Media
Miami | Cleveland | |
Goran Dragic 18 | Scoring | LeBron James 24 |
Goran Dragic 6 | Assists | Isaiah Thomas 6 |
Justise Winslow 10 | Rebounds | LeBron James 11 |
Hassan Whiteside 5 | Free Throws Made | Isaiah Thomas 9 |
Kelly Olynyk 3 | Steals | Isaiah Thomas 4 |
Josh Richardson 2 | Blocks | Tristan Thompson 2 |
Team | Points | FG% | 3PM-3PA | FTM-FTA | Assists | Rebounds | Blocks | Steals | Turnovers |
Miami | 89 | 43.4 | 3-28 | 14-25 | 17 | 52 | 5 | 8 | 20 |
Cleveland | 91 | 35.0 | 6-26 | 29-38 | 18 | 45 | 5 | 9 | 16 |