The Clippers have won three of their four regular-season games against Oklahoma City, the top team in the Western Conference, including a 92-77 victory Monday evening at Staples Center.
They trailed by as many as 11 points before a strong third-quarter push that began with a 6-0 run and finished with Russell Westbrook and Kevin Durant both held scoreless.
The teams entered the fourth quarter tied, 66-66.
Then Blake Griffin and Mo Williams put on a show.
Williams, who entered the fourth quarter scoreless, had 11 points down the stretch. Griffin electrified the crowd with consecutive dunks, sending the Staples Center fans to their feet.
The Clippers, who held the Thunder to 25 points in the second half, earned a playoff berth earlier in the evening when Houston lost to Denver and will make their first postseason appearance since the 2005-06 season.
The Clippers forced Oklahoma City to commit 19 turnovers and held the Thunder to 37.5% shooting from the field.
Nick Young led the Clippers with 19 points on seven-for-10 shooting, including three for four from three-point range.
Westbrook finished with nine points, all of which he scored in the first quarter. Durant had 24 points and five rebounds.
The Clippers, who secured their first playoff berth since 2006, play at Denver on Wednesday.