Duke Johnson rushed for 84 yards and a touchdown for Miami (4-0), which will go into ACC play with its best record in nine years.
Morris injured his ankle early in the second quarter and was replaced by Ryan Williams, who threw for 153 yards and a score. Stacy Coley caught two scoring passes and Dallas Crawford ran for two TDs.
South Florida (0-4) started Penn State transfer Steven Bench at quarterback. He responded with 189 passing yards and one touchdown.
The Bulls tied the score 7-7 in the first quarter on a 3-yard run by Marcus Shaw, but did not score again until the fourth quarter.