After Durant gave the Thunder the lead with two free throws, the Knicks suffered a turnover and then missed their last two shots. J.R. Smith misfired on a jumper just before the buzzer that would have given New York the win.
Oklahoma City held New York to 40 percent shooting while winning its third in a row. The Thunder improved to 3-1 on a five-game road trip that finishes Friday in Charlotte.
Durant scored 34 points, grabbed eight rebounds and handed out six assists, helping the Thunder overcome a six-point deficit heading into the fourth quarter.
New York, which scored just 13 points in the final period, played again without Carmelo Anthony and his sore right knee.
Smith led the Knicks by hitting 14-of-29 shots from the field and scoring 36 points. New York had won its previous two games.