The Clippers edged in front in the second half while holding the Pelicans to 39 percent shooting.
New Orleans has lost the first three games on a five-game road trip that will continue in Portland and Sacramento.
Griffin played 32 minutes, claiming 10 rebounds and handing out five assists. Jared Dudley added 17 points for the Clippers, who moved 2 1/2 games in front of Phoenix at the top of the Pacific Division.
Los Angeles benefited from 36 attempts at the foul line, making 31.