James also had eight rebounds and seven assists in a bruising match-up as Cleveland won in Dallas for the first time in seven years.
"I know I can take more pounding than anybody else on the court tonight," James, who went to the foul line 10 times in the first half, said.
"So I've got to continue to be aggressive and if they (the Mavericks) going to come at us and give hard fouls, I'll give it back."
Zydrunas Ilgauskas added 18 points and 11 rebounds and Larry Hughes contributed 17 points as the Cavaliers won despite shooting only 36.4 percent from the floor while registering a woeful two-of-16 three-point attempts.
In a game where both teams were guilty of poor shooting, Dirk Nowitzki led Dallas with 19 points and 20 rebounds but made only six-of-17 shots from the floor.
Josh Howard also had 19 points for the Mavericks, who managed just 36.5 percent of their field-goal attempts.
Dallas trimmed a 13-point Cleveland advantage to one in the fourth quarter but could not move into the lead.
"We couldn't get timely stops," Mavericks coach Avery Johnson said.
"Somebody would get an offensive rebound or a wide-open shot and on top of it, we just couldn't really score."
Paul Pierce scored 37 points and the Boston Celtics posted a 104-96 road victory over the Seattle SuperSonics. Kevin Garnett added 23 points and 14 rebounds. Kevin Durant led Seattle with 25 points.
Amare Stoudemire scored 30 points and pulled down 15 rebounds in the Phoenix Suns' 108-88 road romp over the Los Angeles Clippers. Corey Maggette topped the Clippers with 21 points.