After the Clippers went on a fourth-quarter run to force overtime, Durant and Westbrook combined to score all 15 Thunder points in the extra session to keep last season's Western Conference champions on top.
Durant finished with a game-high 35 points and Westbrook tallied 23 and nine assists for the Thunder (9-3).
"It was like a playoff game in November," Thunder coach Scott Brooks told reporters. "Everybody laid it all on the line tonight. We did a really good job defensively and that's not an easy thing to do against them."
Los Angeles (8-3) entered the game having won six straight to shoot to the top of the conference, but they were playing catch-up for most of the game in Oklahoma City and could not extend their streak.
Blake Griffin paced the visiting Clippers with 23 points and Jamal Crawford had 20 off the bench.
Chris Paul made just two of 14 shots but the feisty point guard helped Los Angeles outscore Oklahoma City 33-26 in the fourth quarter to force overtime.
"Regardless of what anyone says it's gonna be tough for us to win a game when I play that bad," Paul said. "It's tough because you work so hard but there's just gonna be nights like that."
With the Clippers' Caron Butler out with a shoulder injury, Matt Barnes figured prominently down the stretch on his way to scoring 19 points and grabbing nine rebounds.
He made a three-pointer to pull his team within two points before adding a lay-up to level the score at 102-102 in the final minute.
The Clippers were trying to win seven in a row for the first time since capturing eight straight in 1991. They hold a 1 1/2-game lead atop the Pacific division while the Thunder are three games clear in the Northwest.
Reserve Kevin Martin, who was acquired when Oklahoma City traded away Sixth Man of the Year James Harden just prior to the start of the season, continued his strong play for the Thunder with 20 points.
(Writing by Jahmal Corner in Los Angeles; Editing by Peter Rutherford)