James Rahon added 17 points for the Aztecs (4-1), who led by 12 points at the half and withstood a late USC charge. Xavier Thames (14 points) and J.J. O'Brien (12) also reached double figures as San Diego State drained 7-of-15 three-point attempts.
Franklin also hauled down nine rebounds.
Eric Wise led the Trojans (3-3) with 14 points and seven rebounds.
Dewayne Dedmon added seven points and 10 boards for USC, which shot only 33.3 percent from the field.