The Thunder won their ninth straight, their longest such streak in three seasons, but had to hold on at the end to down the Hornets.
Greivis Vasquez missed a 3-point try for New Orleans in the final seconds would have put the Hornets in front by one and two free throws by Oklahoma City's Thabo Sefolosha put the game away.
Durant scored 35 points and Oklahoma City hit 57 percent of its shots in the second half. New Orleans led by a dozen points late in the third period, but the Thunder took the lead for good on a 3-pointer by Kevin Martin with 6:21 to play.
Martin scored 17 points off the bench and Russell Westbrook added 14 while hitting just 4-of-14 from the field.