Los Angeles stayed close throughout the second half in a bid for the upset, but scored only one point during the final 2:30.
Bosh hit 15-of-22 shots and scored 31 points. James had 13 rebounds and six assists to go with his 27 points.
Miami captured both games in the season series with the Lakers for the first time in franchise history. The Heat won for the fourth time in five games after losing three in a row.
Miami shot 57 percent from the field to help overcome 18 turnovers.