Bryant's one-footed, running 3-pointer with 1:21 remaining in regulation capped the big comeback that saw the Lakers erase a 17-point deficit and force extra time.
The Los Angeles superstar then added six points in the second overtime while Pau Gasol finished with 20 and 14 boards as the Lakers maintained their lead over the Clippers atop the Pacific Division.
Jordan Hill added 14 points and Metta World Peace chipped in with 12 before being ejected in the second quarter for elbowing Thunder guard James Harden in the head.
Oklahoma City, meanwhile, lost despite 35 points from Kevin Durant.
The Thunder came into the contest a half-game behind San Antonio in the race for the top seed in the Western Conference.