Eight-times All-Star James finished with a game-high 32 points and 12 rebounds, and guard Dwyane Wade weighed in with 27 points, as Miami cemented their place at the top of the Eastern Conference with their 15th home win of the season.
The Heat, who outscored the Mavericks 16-6 in overtime, improved their overall record to 22-8 after being tested to the full in a clash of the last two NBA champions.
"Execution going down the stretch was very good," Heat coach Erik Spoelstra said. "LeBron was really big and deep and showing his world-class conditioning level.
"They (the Mavericks) played a very good basketball game. It's not as if we were necessarily letting them score. It was highly competitive at both ends."
O.J. Mayo led the way with 30 points for Dallas while 11-times All-Star Dirk Nowitzki, despite not being back to his best following knee surgery, had 19 points off the bench.
"It shouldn't have gotten to overtime," said Mavericks coach Rick Carlisle, whose team slipped to 13-20 for the season.
"We were up by six with a couple minutes to go and our inability to keep them out of the paint was our downfall."
Dallas made a fast start, surging 12 points clear at 30-18 on the back of a 10-0 run before ending the opening quarter with an eight-point cushion. James earned just six points on three-for-eight shooting from the field.
However, the Heat steadily reeled in the Mavs as James ominously began to find his range and they cut the deficit to 52-50 by halftime at American Airlines Arena.
James poured in a three-pointer to give Miami a 81-79 lead after the third quarter but Dallas regained control and a Mayo three-pointer put them 97-91 up with just over four minutes remaining.
The hosts battled back again and a Shane Battier three-pointer put the Heat 103-101 ahead with 14.5 seconds to go before Nowitski responded with a fadeaway jump shot to take the game into overtime.
After veteran Ray Allen sank another three-pointer, James followed up with a bank shot to put Miami 108-103 up and there was no way back from there for Dallas.
"You've got to respect these other teams," Wade said. "They come in and play very well against us so we've got find ways to win ballgames. That's what it's all about right now."
James, who finished just one assist shy of a triple-double, was presented with the USA Basketball Male Athlete of the Year award by Heat president Pat Riley at half-time.
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