The Heat trailed at halftime but outscored the Bobcats 32-17 in the third quarter, closing the period with an 11-2 run. They never let the Bobcats get closer than seven in the fourth quarter.
It was the Heat's 20th straight win over the Bobcats in the last four seasons, and it completed an 8-0 sweep this season.
The Heat, seeded second in the East, advance to take on the winner of the Toronto-Brooklyn series in the conference semifinals.
James was kneed in the thigh during a collision in the third quarter, but shrugged off the injury and finished 10 of 19 from the field and 10 of 12 from the free-throw line. He also had eight assists and six rebounds.
The Heat also got 17 points from center Chris Bosh, 13 each from guards Dwyane Wade and Norris Cole, and 10 from guard Mario Chalmers.
The Bobcats played without center Al Jefferson, their leading scorer and rebounder. Jefferson suffered a strained plantar fascia in his left foot in Game One and had been hobbled throughout the series.
Guard Kemba Walker led the Bobcats with 29 points. Guard Gary Neal scored 16, forward Chris Douglas-Roberts 14 and guard Gerald Henderson 12.
Charlotte led 27-26 after one quarter and 54-52 at halftime.
For the Bobcats name, it was the final game in franchise history. The team will become the Hornets next season. The Bobcats never won a playoff game in their 10-year history, getting swept in both of their playoff appearances.
NOTES: Bobcats coach Steve Clifford said C Al Jefferson was ruled out because Jefferson couldn't bounce back on just one day's rest, after scoring 20 points in the Heat's 98-85 Game 3 win on Saturday night. Jefferson initially suffered the injury in Game 1. ... The Bobcats had been 16-2 in their previous 18 home games before the Heat's win on Saturday night. ... The Heat have shown killer instinct in the playoffs under coach Erik Spoelstra. They came into Monday's game 11-4 under Spoelstra when they have a chance to close out a series. ... The Heat have won at least one road game in their last 13 straight playoff series, tying the Chicago Bulls (1991-94) for the longest streak in NBA history. ... F LeBron James' 30-point performance on Saturday night marked the 63rd time he has scored 30 or more in the playoffs. Only Kobe Bryant (88) has more among active players. ... Spoelstra said he would like to continue to play G Dwyane Wade about 33 minutes a game and doesn't foresee Wade playing 40 anytime soon. ... The Heat's inactives were C Justin Hamilton and F Michael Beasley, while the Bobcats inactives were C Brendan Haywood and F Jeffery Taylor.