A 14-0 fourth-quarter run, fueled by James and a halfcourt shot from Mo Williams, finally broke the Cavaliers free of the Thunder, who had led by eight points in the first half.
"That was a big momentum-changer," the Thunder's Jeff Green said of the 45-foot shoot that put the Cavaliers up 94-87.
"It was a lucky shot. But those things happen. There's nothing you can do about it."
Williams had eight points, including back-to-back three pointers, and James six points in the spree as the Cavaliers held the Thunder without a point for more than six minutes.
"Any shot like that hurts," Williams told reporters when asked about the halfcourt effort.
"You think you have a big stop. You're down only four. Then all of a sudden, you're down seven. It takes the life out of you."
James knocked down five three-pointers and had seven rebounds, six assists and four steals for the Central Division-leading Cavaliers, who improved to 17-7.
"He was in a zone, there was no doubt," Thunder coach Scott Brooks said. "You can't do much about it. He's one of the best players in the world. We couldn't guard him any closer."
Center Shaquille O'Neal was back in the line-up after getting hit in the face in Friday's game against Portland and experiencing blurred vision. He played 18 minutes, had six rebounds, two blocked shots and five points.
Kevin Durant had 29 points and Green 26 for Oklahoma City (12-10), who have shown steady improvements after finishing last season bottom of the North West division with a 23-59 record.
"They're a totally different ballclub," Williams said of the Thunder. "Those young guys are growing up ... It's no secret why they're winning games right now."
(Reporting by Gene Cherry in Salvo, North Carolina. Editing by Patrick Johnston)