"We know we can win against good teams, and we showed it," Rams quarterback Skyler Locklear said.
Omarion Hampton accounted for all five first-half touchdowns for the Rams, who broke open a game that was evenly contested for much of the first half.
After Hampton's second score, Garner answered with a 3-yard touchdown run by Derrick Alston and a two-point conversion to tie the score at 14-14.
Cleveland again took the lead when Locklear hit Hampton with a 79-yard touchdown pass but the Trojans responded with a 31-yard TD pass of their own when Daveon Dunn found Russell Sanders for the score.
But again, it was Hampton, scoring again to put the Rams up for good.
"We had like a talk, with the team, and we were just like, it was a focus thing," Hampton said.
Cleveland earned its third consecutive victory against Garner.