James scored 19 points after injuring his thigh in the third quarter. He finished the game 10 of 19 from the field and had nine assists.
Chris Bosh added 17 points and Dwyane Wade battled through foul trouble and finished with 15 as Miami won its 20th consecutive game over Charlotte.
The two-time defending champion NBA champions will await the winner of Brooklyn-Toronto series, which is tied 2-2.
Kemba Walker led Charlotte with 29 points.
The Bobcats played without Al Jefferson, their leading scorer and rebounder who has been bothered by a foot injury since the first quarter of Game 1.
The loss signaled the end of an era for the Bobcats. They will become the Hornets next season.
The Heat improved to 16-2 in first-round games since James’ arrival four years ago.
Miami began to take control midway through the third quarter shortly after James gave his teammates a scare when he drove to the basket and his right thigh collided with Bismack Biyombo’s knee.
James remained on the floor for more than a minute and concerned teammates began gathering around him. He eventually got up and hobbled to the bench and sat down during a timeout, but he stayed in the game.
The injury only seemed to inspire James after fans cheered when he went down.
After the timeout he buried a 3-pointer and a long jumper before a one-handed dunk to help give Miami a 73-66 lead with 4:51 left in the third quarter. Miami pushed the lead to 13 when Norris Cole knocked down a 3-point buzzer-beater at the end of the quarter.
Charlotte never got closer than seven points in the fourth quarter.
With Wade on the bench for most of the fourth quarter with foul trouble, the Heat went almost exclusively to James. The four-time NBA MVP scored 11 points in the final period and Cole and James Jones knocked down big 3-pointers to keep the Bobcats at bay.
Despite being without Jefferson, the Bobcats led 54-52 at halftime behind 12 points from Walker.
Walker, who finished 11 of 15 from the field, did a little bit of everything to keep Charlotte in the game.
With the shot clock winding down on one possession he purposely fired the ball off the backboard from just inside the 3-point arc and raced to get his own rebound and put it in. On the next possession, Walker drove the lane and found Biyombo with a no-look feed for a dunk.
Before the game the Heat showed solidarity with the Los Angeles Clippers over the Donald Sterling controversy.
Like the Clippers on Sunday, the Heat ran out of the tunnel wearing their warmups, huddled at center court and tossed their white shooting T-shirts to the ground. They then went through their pregame routine with their red Heat warmup jerseys inside out, hiding the team’s logo.