Stewart finished 12 of 17 for 196 yards before giving way to McCoy Hill after intermission. Stewart threw a pair of first quarter touchdown passes to Mitch Mathews, of 71 and 15 yards, and ran 16 yards for a score to build a 21-0 lead.
It was more of the same in the second, as Stewart connected with Terenn Houk from 9 yards and Jordan Leslie from the 1 - after BYU recovered a fumble near the goal line. Stewart later ran for a 6-yard score and Nate Carter pushed one in from the 2.
Adding insult to injury, the Cougars (7-4) capped the half by blocking a punt through the end zone for a safety.
Savannah State (0-12) gained a mere 63 yards.