Martinez ran 15 times for 166 yards and two TDs and passed for another as the Huskers turned back an upset bid by the Bulldogs, who were four-touchdown underdogs.
Derek Carr threw incomplete to a well-covered A.J. Johnson on a 2-point try after his 26-yard TD pass to Josh Harper pulled the Bulldogs to 28-26.
Abdullah, who set a school record with 211 kick return yards, then made the biggest play of the night to break open the game.
Fresno's Robbie Rouse ran 36 times for 169 yards and Carr was 20 of 41 for 254 yards.
The Associated Press contributed to this report.