Houston rallied from 13 points down early in the fourth period to within five in the closing minutes, but could not overcome the 1-2 scoring punch of the Heat.
James scored 32 points while Wade had five rebounds and eight assists to go with his 31 points. Miami won its third in a row and improved its home record to 20-3.
James Harden scored 36 points with 12 rebounds and seven assists to lead the Rockets. Houston, which equaled a league record with 23 3-pointers on Tuesday in a win over Golden State, was 9-of-25 from long range against Miami.