Serge Ibaka scored 14 points for the second-seeded Thunder, who took a 3-1 series lead and moved to the brink of their second straight trip to the Western Conference finals.
Oklahoma City improved to 7-1 in the post-season with a tenacious rally on the second night of back-to-back games against the Lakers and Kobe Bryant, who scored 38 points in Los Angeles' fifth loss in seven games overall.
The Thunder finished Game 4 on a 22-8 run, punctuated by Durant's three-pointer and two late free throws from James Harden, who had 12 points.
Game 5 is Monday night in Oklahoma City.
SPURS 96, CLIPPERS 86
Tim Duncan scored 19 points, helping engineer a 24-0 run in the third quarter after the San Antonio trailed by 24 points, and the Spurs beat Los Angeles to take a 3-0 lead in their second-round playoff series.
Tony Parker added 23 points, rookie Kawhi Leonard 14 and Manu Ginobili 13 to help the top-seeded Spurs win their 17th in a row and improve to 7-0 in the playoffs.
Blake Griffin had 28 points and 16 rebounds, and reserve Mo Williams added 19 points for the Clippers, who face some daunting NBA history heading into Game 4 on Sunday at Staples Center. No team has ever rallied from a 3-0 deficit to win a series.