The Thunderbirds (5-2, 4-0 Big Sky) have won five-straight, and are tied with Eastern Washington (5-2, 4-0) atop the conference.
Olsen threw for 336 yards and ran for a 1-yard score. Malik Brown had 12 carries for 90 yards with a 31-yard touchdown run midway through the third quarter.
Southern Utah's James Cowser sacked quarterback Ben Scott at the Aggie 27 that forced a fumble. Chance Bearnson recovered, and Olsen connected with Justin Brown on a 13-yard scoring strike two plays later to make it 20-6 late in the third quarter.
Ty Rutledge ran for a 2-yard score, and Steven Wroblewski had a 17-yard touchdown catch in the fourth quarter.
Brady Stuart kicked field goals of 33 and 48 yards for UC Davis (1-7, 1-4).