Then Dallas lost a major advantage when forward Josh Howard has aggravated his problematic left ankle and left the game.
Howard missed 11 games earlier this season with the ankle injury and wound up wearing a walking boot to help with his recovery.
Durant had already missed the Thunder's last game with a sprained right ankle and was joined on the sidelines by Green, who started having back spasms Monday.
Durant is fourth in the NBA with a 26-point scoring average, while Green is second on the team with 17.2 points a game.
"Kevin and Jeff are our best offensive players. They've proven that most of the year," Thunder coach Scott Brooks said. "Our guys that work hard before practice and after practice and before games are going to get an opportunity to fill in the offensive void."
"I know young guys' bodies heal a lot quicker than the older guys and mentally they think they heal quicker also. But we're going to make sure he's 100 percent before he steps on the court," Brooks said of Durant.
Green had played in 93 straight games since he missed two with a sprained left ankle in February 2008.
Howard started Monday night's game and scored seven points before halftime but was not a part of Dallas' lineup to start the second half.
Howard is the Mavericks' third-leading scorer with an average of 18.3 points.
Information from The Associated Press was used in this report.