James connected on 11-of-14 shots from the field and Dwyane Wade had a double-double of 21 points and 12 assists as the Heat notched a seventh straight win.
Ray Allen helped Miami pull away in the fourth quarter, netting nine of his 17 points down the stretch.
Phoenix got a balanced scoring attack, led by Channing Frye with 16 points and eight rebounds, but couldn't keep up with the two-time defending NBA champions.
Goran Dragic supplied 14 points, nine assists and eight rebounds for the Suns.
Notable deaths of 2014 [PHOTOS]
Spurs hit the road to battle high-flying Suns