Los Angeles bounced back from an overtime loss 24 hours earlier to Dallas by pulling away in the final 12 minutes.
The Clippers held only a two-point lead heading into the final period, but limited New Orleans to 14 points in the quarter.
Griffin scored 19 points while Chris Paul had 16 points and nine assists. Los Angeles has won three out of four.
New Orleans, which had won three straight, was led by 24 points from Eric Gordon.
Los Angeles began the fourth period on a 10-2 run and was not threatened again. The Clippers made 13 shots from 3-point range to just four for the Hornets.