Franklin grabbed seven rebounds and Thames connected on five 3-pointers as the Aztecs (5-1) claimed a win in the John R. Wooden Classic.
Deshawn Stephens supplied 12 points and six rebounds for San Diego State, which marked its 26th straight decision against a California opponent.
The Bruins (5-3), meanwhile, lost for the second time in four games.
Jordan Adams scored 23 points and Shabazz Muhammad added 16 in UCLA's defeat.
Celebrity Families of 2014 [PHOTOS]