MIAMI - Eddie Jones scored 25 points and Lamar Odom added 14 points and 10 assists, helping Miami become the final NBA team to break into the victory column.
LeBron James had 18 points on 6-of-15 shooting for Cleveland, which lost its 26th straight road game since February and failed in its bid for the franchise's first three-game winning streak since April 2002.
Zydrunas Ilgauskas added 20 points for the Cavaliers, and Carlos Boozer had a game-high 16 rebounds.
The Heat lost their first seven games, the franchise's worst start since going 0-17 to open its inaugural season of 1988-89. They missed their last five shots, giving the Cavaliers plenty of chances to pull off a late rally.
But James was stifled on three key possessions, committing an offensive foul with 2:08 left, having a shot blocked by Udonis Haslem with 1:30 remaining and failing to handle a quick pass from Ilgauskas with 18.5 seconds left.