Matt Carroll added 17 points, Raymond Felton scored 13, Adam Morrison had 10 points and Emeka Okafor pulled down nine rebounds for the Bobcats (1-2), who gave Sam Vincent his first win as an NBA head coach.
Daequan Cook scored 10 points to lead the Heat (0-4), who gave up 30 points off turnovers.
Former NBA MVP Shaquille O'Neal had six points and three rebounds in the first quarter for Miami, but left the game in the closing seconds of the period with what team officials said was a bruised left quadriceps.
Miami hit five of its first six shots in the opening minutes to race out to an 11-6 lead, but Wallace scored six points during a 16-2 run that put Charlotte ahead 22-13 with 3:33 remaining in the first quarter.
Felton's jumper with 7:09 left in the second quarter capped an 11-2 run to put the Bobcats up 40-23, and his three-point play in the final seconds put Charlotte up 52-36 at the break.
The Bobcats took their biggest lead of the game late in the third quarter, going up 67-43 with 3:30 remaining on Jameel Watkins' tip-in of Okafor's missed hook shot.