The Thunder ended the game on a 16-4 run that began when Durant made a hook shot with 5:28 to play to bring Oklahoma City within six.
Two free throws by Serge Ibaka with 1:56 remaining put Oklahoma City in front for good.
Russell Westbrook added 22 points and a season-best 13 rebounds for the Thunder. It was Oklahoma City's sixth straight win and improved its road record to 13-6, best in the Western Conference.
Philadelphia lost for the eighth time in 11 games and failed to build on Tuesday's runaway victory over Detroit. The 76ers made just 8-of-27 shots in the fourth quarter.
Andre Iguodala and Jrue Holiday both had 18 points for Philadelphia.