The Thunder won their sixth in a row, a streak that began after losing a dramatic decision to the Warriors.
Serge Ibaka missed a jumper from the foul line with 5.9 seconds to go in the extra period that would have tied the game. Westbrook fought for the rebound and almost lost it out of bounds, but Jeremy Lamb saved it to Westbrook.
Westbrook then dribbled beyond the 3-point line and hit a shot from the corner to give him 34 points for the game.
Oklahoma City remained unbeaten at home in eight games while Golden State suffered its second straight loss.
Kevin Durant contributed 25 points and 13 rebounds while Ibaka had 18 points and 13 boards.
Stephen Curry led the Warriors with 32 points, 11 rebounds and five assists while Harrison Barnes had 26 points.