What a magical season it was was Steve Sarkisian and the 1996 BYU Cougars. That season the Cougs went 14-1 (the lone loss was at Washington. The NCAA rules were different back then and a team could play in week 1 and not have it count against your total number of games. Also, BYU played at Hawaii and they got an extra game because of it (similar to the rule that exists now). They played in the WAC Championship game (a win against a very good Wyoming team).
Now, to the Cotton Bowl. BYU entered the game ranked #5 in the country against Kansas State, who came into the match ranked #14. Defense dominated the game, with BYU limiting the Wildcats to 199 yards through the first 3 quarters (113 of that on 2 plays). The Cougars trailed 5-15 going into the 4th but answered with two touchdowns in the quarter to pull out the victory, 19-15. Sark hit K.O. Kealaluhi on a post route to the corner of the endzone.
Apologizes for the poor quality. This was the only version I could find. Please leave your thoughts/ memories in the comments section below.
As an aside, I change my SB Nation account handle to kwlarson but it hasn't been approved for posting stories yet. So I am using my old account. (This is week 2 and waiting.)