The Clippers led by as many as 19 points early in the fourth quarter, but the Lakers went on a 24-7 run that brought them within two with 1:29 to play.
That comeback began to run out of steam, however, when Paul hit two free throws and a jumper to create a six-point advantage with 19 seconds left.
It was one of the most anticipated games of the NBA season with the Clippers trying to establish dominance after suffering at the hands of the Lakers for years.
In their first meeting this season the Clippers emerged with a 105-95 victory.
The Clippers snapped a two-game skid which followed a 17-game winning streak. The Lakers have dropped two in a row, now stand two games under .500 and are 10 games behind the Clippers in the Pacific Division with the season almost 40 percent completed.
Paul scored 30 points, although he hit just 11-of-25 shots from the field, and Blake Griffin added 24 for the Clippers.
Bryant led the Lakers by making 15-of-25 shots and scoring 38 points, Dwight Howard contributed 21.