John Wall missed a driving layup at the buzzer for the Wizards, who were seeking a third straight win.
Oklahoma City trailed, 92-82, with 3:26 left with the fourth quarter, but went on a 14-4 run, capped by Durant's straightaway three-pointer with 13.6 seconds left.
Beal missed a running 12-footer at the buzzer.
In overtime, Durant blocked a shot by Wall and streaked toward the other basket. He made both free throws for a 106-105 lead with 40.7 seconds left.
San Antonio 120, at New York 89: