League MVP Durant began the game with one-for-seven shooting from the floor, but caught fire and added 16 rebounds and five assists in a Game Six road win that gave the Thunder a 4-2 best-of-seven series triumph.
"It's not how you start, it's how you finish," Durant told reporters. "I just tried to stay with it, no matter what. My team mates did a great job screening for me."
Durant's assured performance carried the Thunder to a third West final in four years, in which they will play the top-seeded San Antonio Spurs.
It was far from easy going for Oklahoma City, however, as they had to rally from an 11-point deficit in the third quarter to muscle past the Clippers.
In Game Five, the Thunder were down by 13 in the closing minutes of the fourth but fought back to stun Los Angeles.
The Clippers' Chris Paul, who took most of the blame for that loss with several bad plays in the final few moments, had 25 points and 11 assists in their season-ending defeat.
Blake Griffin added 22 points and eight rebounds.
For Los Angeles, it was a post-season of drama, starting when owner Donald Sterling made racial comments that got him banned for life from the NBA.
"We've gone through a lot of stuff over the last three or four weeks," Clippers coach Doc Rivers said. "I don't think that's why we didn't win. I don't think we should use that as an excuse."
For the Thunder, Game Five hero Russell Westbrook made just 4-of-15 shots from the field but recorded 19 points and 12 assists.
It was also a solid night for the Oklahoma City bench, although the team lost forward Serge Ibaka to a calf injury in the third quarter.
The Thunder made their push in the third after trailing early, with Oklahoma City using a 7-0 run at the end of the quarter to tie the game at 72-72 before carrying the momentum into the fourth.
As a whole, the Thunder out-scored the Clippers 62-48 in the second half.
(Writing by Jahmal Corner in Los Angeles; Editing by Peter Rutherford)