Durant's off-balance floater bounced on the rim, caromed off the backboard and through the net, handing a dramatic victory to the second-seeded Thunder in the opener of their Western Conference quarterfinal series.
The game-winner came after Dirk Nowitzki had given the Mavericks a one-point lead in a pair of free throws with 9 seconds to go.
Durant ended with 25 points on 10-of-27 shooting from the field. Russell Westbrook led Oklahoma City with 28 points and five assists.
Serge Ibaka contributed 22 points, six rebounds and five blocked shots for the winners.
Nowitzki scored 25 points and Jason Terry came off the bench to add 20 for Dallas.