Griffin scored 16 points with six rebounds and Paul added 15 points to go with eight assists as the Clippers extended their winning streak to three games.
Caron Butler supplied 13 points and helped out underneath the basket with six rebounds for Los Angeles.
The Hawks, meanwhile, dropped their second consecutive game despite 13 points and six rebounds from Josh Smith.
Atlanta's Al Horford was held to 11 points and nine boards.
Notable deaths of 2014 [PHOTOS]