The Thunder stormed back from a 13-point, fourth-quarter deficit and had a chance to tie it on Kevin Durant’s 7-footer along the left baseline with 10 seconds left.
James provided the defense on the shot and rebounded the miss before getting fouled and hitting two clutch free throws.
The series is tied at a game apiece heading into Game 3 on Sunday night in Miami.
James hit all 12 of his free-throw attempts and was 10 of 22 from the field. He added eight rebounds.
James had come under fire after Tuesday’s Game 1 loss for disappearing in the fourth quarter, scoring only seven points. This time, he was a factor as the Heat held off the charging Thunder.
Durant finished with 32 points, hitting 12 of 22 shots from the field and four of six free-throw attemps.
Russell Westbrook had 27 but the Thunder weren’t able to overcome a double-digit deficit.
Former Georgia Tech star Chris Bosh made his first start in the playoffs and scored 16 points and added 15 rebounds.
After coming off the bench in the first four games since returning from an abdominal injury, Bosh was back in the starting lineup. He replaced Udonis Haslem.
Bosh had started every game he played in throughout the regular season and the playoffs before missing nine games with a strained lower abdominal muscle during the Eastern Conference semifinals and finals.
Coach Erik Spoelstra said after Bosh scored 10 points off the bench in Game 1 that the Heat “need more from him offensively” and the Heat got that Thursday night.