"I know the guys were happy for me," Oden added. "I definitely felt love. And I'm excited that they were there for me."
Heat Coach Erik Spoelstra said Oden's face "lit up" when he told him he was going to put him in the game.
"We are just so pleased for him," Spoelstra said. "It was just great to see him do something he loves to do. It was taken away from him for four years. We just continue to make patient, steady progress forward from here."
James scored 27 points and Dwyane Wade added 25 for the Heat, who trailed after three quarters but opened the fourth with a 21-2 run.
Wade hit a 3 during the decisive surge, then stole the ball for a breakaway jam. Ray Allen did all his scoring with three straight 3s to make it 98-84.
Chris Bosh had 14 points and nine rebounds for Miami (5-2), and Chris Andersen added 13 points.
Eric Gordon scored 19 for New Orleans (6-1), while Anthony Davis had 18 points and eight rebounds. Anthony Morrow added 16 points, Jrue Holiday 12 and Ryan Anderson 10.