Irving crashed down into the paint to contest Johnson's slam, but the 6-foot-8, 240-pound forward reached back and decimated the rim and an outstretched Irving.
The Heat took a 61-43 lead into halftime. Johnson had seven points, three assists and two rebounds in 12 minutes.
Irving dropped 17 points with two assists and two rebounds in the first half.
Miami shot 53.1 percent from the floor, and the Celtics were 19-for-49 (38.8 percent) from the field after two quarters.