Durant scored 17 of his 36 points in the fourth quarter and Westbrook finished with 27 for the game and added 11 assists.
The Thunder held Miami to 19 points in the third quarter and outscored the Heat 31-21 in the fourth, after the Heat had led by seven at half time. Westbrook and Durant outscored the entire Miami team in the second half 41-40.
Oklahoma City also won the rebounding battle 43-35 and outscored Miami in transition 24-4.
Game 2 will be played in Thursday Oklahoma City.
Notable deaths of 2014 [PHOTOS]