Ajay Mitchell scored 24 points and handed out 10 assists without a turnover to help the Thunder take a 3-0 stranglehold on the best-of-seven Western Conference semi-final series.
The Lakers will host Game 4 on Monday, trying to become the first NBA team to rally from 3-0 down to win a playoff series.
"I'm not giving up on this series," defiant Lakers coach JJ Redick said. "We're going to try to win on Monday. We're going to try to extend the series and we're going to try to take this thing back to OKC."
But the Lakers, still without injured scoring champion Luka Doncic, couldn't conjure a crucial win as their series shifted to Los Angeles.
Rui Hachimura led the Lakers with 21 points, and James added 19 points, six rebounds, and eight assists.
But the Thunder's depth was just too much for the depleted Lakers.
"That's the strength of their team," Redick said.
With reigning Most Valuable Player Shai Gilgeous-Alexander connecting on just seven of 20 shots from the floor, second-year guard Mitchell -- starting in place of injured Jalen Williams - stepped up.
"He's a gamer," said Gilgeous-Alexander, who finished with 23 points. "It might be a shock to the world, but this is no shock to us."
As in game two, the Lakers took a two-point lead into half-time, this one largely on the strength of 11 first-half three-pointers.
But again the Thunder exploded in the third period, opening the second half on a 21-6 scoring run.
After that, it was all but over. The Lakers connected on just eight of 22 shots from the field in the third period, including just one from three-point range. Their turnovers began to mount, and the Thunder pushed their lead to as many as 27 in the fourth quarter.
Gilgeous-Alexander said the Thunder, who swept the Phoenix Suns in the first round, will "absolutely" be aiming to finish off the Lakers on Monday.
"We would never want to waste an opportunity to win a basketball game," he said. "We've got to do the same thing we did in the first three games - be the aggressor, play the right way together."