Shai Gilgeous-Alexander scored 24 points to lead the Thunder and Isaiah Joe added 23 off the bench as six Thunder players scored in double figures in a convincing 128-109 victory.
The Warriors had seven players score in double figures, with Jonathan Kuminga leading the way with 21 points and six rebounds.
But sharp-shooter Klay Thompson made just one of his 11 shots from the floor on the way to five points.
Warriors star Curry was again sidelined with a troublesome knee while Green was serving the first game of his five-game suspension for grabbing Minnesota's Rudy Gobert around the neck during a loss to the Timberwolves on Tuesday.
Warriors coach Steve Kerr told reporters before the game that Green, who was ejected after throwing an arm around Gobert's neck and dragging him across the court, "definitely took it too far."
Kerr said he had no objection to Green reacting to Gobert's contact with Golden State's Thompson - after Thompson tangled with Minnesota's Jaden McDaniels - but he said Green crossed a line.
"He hung on for six, seven seconds. It was a terrible visual for the league, for Draymond, for everybody," Kerr said. "Draymond was wrong, he knows that, it's a bad look. The five games is deserved. We move forward."
But without Green, the Warriors defence was clearly lacking against a young, hungry Thunder team.
Joe connected on seven of seven attempts from three-point range on the way to his season high in scoring.
Josh Giddey added 19 points, rookie Chet Holmgren chipped in 13 points and 10 rebounds in his fourth career double-double and the Thunder notched their fifth win in six games.
Oklahoma City led by as many as 15 points in the first quarter. Golden State trailed by nine entering the fourth, when the Thunder out-scored them 34-24 to roll to victory.
In the day's only other game, Jimmy Butler scored 36 points to help the Miami Heat shake off a slow start and beat the Brooklyn Nets 122-115, pushing their winning streak to seven games.
The Heat, with Tyler Herro still sidelined by injury, missed 10 of their first 11 shots, but the Nets couldn't build a lead of more than six points in the first quarter.
By half-time, the Heat were up 60-52, and Butler scored 18 in the third quarter as Miami pushed their lead to double digits, never trailing in the second half.
Butler connected on 12 of 19 shots from the field and added five rebounds with three assists and three blocked shots.
"Whatever it takes to win," Butler said. "I think we did a good job in the second half of guarding. I was very, very, very proud of us for that.
"I don't think we rebounded as well in the fourth quarter, but overall we played some great basketball.
Duncan Robinson scored 26 points for Miami and Bam Adebayo chipped in 20.
Mikal Bridges and Lonnie Walker IV scored 23 points apiece for the Nets, whose November 1 victory over last year's Eastern Conference champions had pushed the Heat to 1-4.
Miami haven't dropped a game since and have climbed to third place in the East, 1.5 games behind leaders Boston.