Westbrook's 19-footer came 1:12 into the extra frame and put Oklahoma City ahead for good as Portland went cold, connecting on only 1-of-9 shots from the floor in overtime.
Westbrook also prevented the Trail Blazers from winning in regulation with a block of Nicolas Batum's drive to the hoop in the closing seconds.
The Thunder had tied the game 6 seconds earlier when LaMarcus Aldridge drew a controversial goaltending call on Kevin Durant's layup attempt.
Durant pumped in 33 points while Westbrook added 28 points, 11 rebounds and eight assists for Oklahoma City.
Aldridge finished with 39 points for the Blazers, who lost for only the second time in 13 home games.