LeBron James led the Heat with 26 points, Bosh finished with 22, Dwyane Wade scored 17 and Mario Chalmers added 12 for Miami, which has beaten the Bobcats 14 straight times.
Kemba Walker scored 27 points for the Bobcats, who had led the entire second half until Bosh's barrage.
At Oklahoma City, Kevin Durant recorded his first triple-double of the season with 32 points, 10 rebounds and 12 assists as the Thunder rallied for yet another fourth-quarter win, beating the Minnesota Timberwolves 113-103.
Oklahoma City extended its winning streak to seven games, tops in the Western Conference, and moved to 9-0 on the season at home. It's the franchise's longest home winning streak to open a season since the 2004-05 campaign, when the team played in Seattle.
Kevin Martin, in his return to Oklahoma City after joining Minnesota during the offseason, led the Timberwolves with 24 points, while Nikola Pekovic had 22 points and 10 rebounds.
The New Orleans Pelicans overcame the loss of Anthony Davis to a broken left hand to beat the New York Knicks 104-99 after Ryan Anderson made seven 3-pointers and scored 31 points.
Tyreke Evans added 24 points, including 10 in the fourth quarter, as the Pelicans sent the Knicks to their ninth straight loss overall and seventh in a row at home.
Davis had seven points and four rebounds in the first quarter before leaving with what the Pelicans said was a non-displaced fracture in his left hand. The team said a timetable for his return has not been determined.
Carmelo Anthony finished with 23 points and rookie Tim Hardaway Jr. had 21 for the Knicks.
In other games, the Golden States edged the Sacramento Kings 115-113, the Portland Trail Blazers beat the Los Angeles Lakers 114-108, the Detroit Pistons defeated the Philadelphia 76ers 115-100 and the Denver Nuggets were 112-98 winners over the Toronto Raptors.
