James grabbed nine rebounds, Dwyane Wade added 31 and 11 rebounds and Chris Bosh chipped in with 11 points and four rebounds for Miami.
The Heat won for the 18th time in 19 games overall and notched their 11th consecutive road victory.
They were led by Stephen Jackson's 22 points while D.J. Augustin contributed 16 points.
Wisconsin business offering 'therapeutic cuddling' forced to close
Police: Sword-wielding man demanded free tacos