Nick Young led a balanced attack with 19 points off the bench, Blake Griffin added 17 and 11 rebounds and the Clippers overwhelmed the visiting Thunder in the second half to reach the post-season for the first time since the 2005-06 campaign.
"It feels great, especially to do it against one of the top teams in the league," Young explained.
"I was too excited after the game. I ran to the back and was slapping hands with everyone."
Winners in 12 of their last 14 games, the Clippers (38-23) also have a shot at their first ever division title, trailing the Lakers by a game in the Pacific Division, and for third in the West.
The Thunder (44-17), meanwhile, slipped percentage points behind San Antonio in their see-saw tussle for the top seed in the conference.
Kevin Durant had a team-high 24 points for Oklahoma City, who built a nine-point halftime lead before being outscored 49-25 in the second half.
It was their second defeat at the hands of the Clippers in less than a week following a two-point loss last Wednesday.
In the latest showdown, Los Angeles scored the game's first basket and did not lead again until the fourth quarter, and as the Clippers warmed up to pull away, the Thunder suddenly went cold and shot just 37 percent on the night.
All-Star Russell Westbrook had a particularly off game and finished with just nine points.
Chris Paul tallied 12 and 10 assists. His arrival to the Clippers through an off-season trade, combined with the team's other roster moves, signalled new promise for a franchise that has endured too many losing seasons.
"It means a lot for us to make the play-offs but we can't be complacent, we have to keep pushing forward and want more," Griffin said. "We still have a lot of work to do."