Paul finished with 24 points and 12 assists. Griffin also scored 24 points to go with 12 rebounds.
Jamal Crawford came off the bench to put in 20 points for the Clippers, who secured their first-ever Pacific Division title at the expense of their Staples Center rivals.
The win also gave the Clippers a season-series sweep of the Lakers for the first time since 1974-75, when the franchise was known as the Buffalo Braves.
The victory allowed them to exit a short list of NBA teams never to have won a division crown, which now includes only the Memphis Grizzlies and Charlotte Bobcats.
Kobe Bryant and Dwight Howard each provided 25 points for the Lakers, who remained percentage points out of the Western Conference's eighth and final playoff spot. Bryant also piled up with 10 assists and seven rebounds.