Durant took an inbounds pass and nearly lost control of the ball but recovered, took two dribbles and buried the go-ahead basket.
DeMar DeRozan's heave at the buzzer didn't draw iron and the Thunder held on for their fifth win in six tries.
Durant finished 7-of-12 from 3-point range and also had 12 rebounds and seven assists.
Reggie Jackson added 25 points and 12 rebounds and Serge Ibaka had 13 points in the win.
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