James scored Cleveland's first five points of the second overtime to put the home team into a 106-102 lead, an advantage they would never relinquish.
He also had eight assists and three blocked shots in the game.
"My team needs me to make big plays down the stretch and that's what I did," James said.
"It wasn't just me though, everybody made plays." Gerald Wallace led the Bobcats with 27 points and 12 rebounds.
Raymond Felton's three-pointer for Charlotte forced the first overtime with a three-pointer by Cleveland's Damon Jones leading to the second.
The Boston Celtics improved to 30-4 with an 86-77 road win over the New Jersey Nets. Kevin Garnett had 20 points and 11 rebounds for the league-leading Celtics while the Nets scored only seven points in the final 11 minutes of the fourth quarter after leading 70-63.
Bobby Jackson's career-high seven three-pointers and 25 points led the New Orleans Hornets to a 114-88 rout of the Miami Heat , who lost their 10th in a row.
Chris Bosh's 40 points and 11 rebounds powered the Toronto Raptors to a 99-90 victory over the New York Knicks, who lost their fifth consecutive game at home.
The Houston Rockets rolled to their fifth consecutive win, beating the Minnesota Timberwolves 113-82. Luis Scola led the Rockets with 22 points and nine rebounds. Yao Ming had 15 points.
Carmelo Anthony had 32 points and 11 rebounds and Allen Iverson contributed 21 points and 13 assists in the Denver Nuggets' 113-103 home win over the Orlando Magic.
The Los Angeles Lakers cruised to a 110-105 home win over the Milwaukee Bucks behind Kobe Bryant's 37 points. Andrew Bynum added 25 points and 17 rebounds.
Golden State Warriors beat the Memphis Grizziles 116-104 despite 43 points from Pau Gasol. Baron Davis had 20 points and 19 assists for the Warriors.
Andres Nocioni's 26 points helped the Chicago Bulls hand the Philadelphia 76ers their sixth successive loss, a 100-97 defeat in Philadelphia.
Antawn Jamison scored 22 points and Caron Butler 21 in the Washington Wizards' 102-98 overtime victory over the Atlanta Hawks, who were led by Josh Smith's 35 points. The loss came hours after the NBA ruled the Hawks must replay the final 51.9 seconds of a victory over the Miami Heat last month because a home scoring crew incorrectly fouled out Miami's Shaquille O'Neal when he actually had five fouls.