James scored 24 points at Crypto.com Arena in LA, while Shai Gilgeous-Alexander, the current MVP, scored 35 points and contributed eight assists for the Thunder.
The Thunder, who beat the Phoenix Suns 4-0 in the first round of the play-offs, will play the Minnesota Timberwolves or the San Antonio Spurs – their semi is level at 2-2 – in the Western Conference final.
In the Eastern Conference semi-finals, the Cleveland Cavaliers earned a 112-103 home win against the Detroit Pistons to level their series at 2-2.
Donovan Mitchell scored 43 points at Rocket Arena for the Cavs, who lost the first two games in the series.
Mitchell scored 39 in the second half, equalling the record – set by Eric Floyd of the Golden State Warriors in 1987 – for the most points in one half of a post-season game.
The Cavs or the Pistons will play the New York Knicks in the Eastern Conference final.