Kobe Bryant scored 38 points and Dwight Howard had 21 points and 15 rebounds for the Lakers, who lost for the second time this season to their Staples Center co-tenants.
Bryant carried the Lakers in the fourth quarter when they closed to 99-97 on his 23-foot jumper with 1:29 left. But Paul scored the Clippers' final eight points to seal the victory and drop the Lakers two games below .500. The Clippers lead the Lakers by 10 games in the standings.
The Lakers continue to struggle under new coach Mike D'Antoni. They've lost three of their last four games.
The Clippers shot 50 percent and outscored the Lakers 52-36 in the paint.
Bryant scored 16 points in the fourth, when the Lakers rallied from 19 points down. The Clippers fouled for much of the final 5:51, and the Lakers made 10 of 12 free throws. Howard missed two foul shots but then made two to get the Lakers within four before Bryant's jumper got the Lakers the closest they had been since early in the game.
But Paul closed with a flourish, including a 6-for-6 stretch at the line, while Bryant's 3-pointer went in and out with 43 seconds to go.
The Lakers got within three early in the third only to have the Clippers push their lead to 10 points. It was a similar situation in the second, when the Lakers got within five points on Bryant's 3-pointer before the Clippers ran their lead back to 10 points by halftime.
The first three quarters were punctuated with several highlight dunks from both sides. Paul fed DeAndre Jordan and Griffin on alley-oop slams that had the sellout crowd of 20,179 roaring.
The Clippers had dropped two consecutive road games earlier in the week, when their 17-game winning streak was snapped.
Jodie Meeks scored 14 points for the Lakers and fellow reserve Jordan Hill had 13 before he sprained his right ankle early in the fourth.