Muema had 105 yards on 14 attempts, and Katz was 16 of 22 passing for 181 yards for the Aztecs (4-3, 2-1 Mountain West), who were not penalized in a game for the first time since 1973.
Conner Smith was 18 of 22 for 165 yards and an interception for the Rams (1-6, 0-3).
SDSU converted all three of Colorado State's turnovers into touchdowns, and scored another TD after the Rams gave the ball up on downs.
On the first play from scrimmage in the second half, Marquise Law fumbled for Colorado State, and Jake Fely recovered for the Aztecs. Two plays later, Katz scrambled to the end zone from 11 yards out to give SDSU a 24-7 lead.
Largent had two interceptions and Fely two sacks for the Aztecs, who have won seven of the last eight meetings between the teams.