Mariota tied a school record with the six-TD performance, going 27-of-34 for 377 passing yards.
Kenjon Barner overcame an injured right hand while rushing for 65 yards on 20 carries for Oregon.
With their 13th straight triumph, the Ducks (10-0, 7-0 Pac-12) boosted their hopes of claiming the top spot in the Bowl Conference Series rankings after current No. 1 Alabama lost to Texas A&M Saturday.
Oregon must face No. 15 Stanford next Saturday before finishing the regular season at 12th-ranked Oregon State.
The Golden Bears (3-8, 2-6) dropped their fourth straight as Allan Bridgford was held to 9-of-21 through the air for 113 yards, a touchdown and two interceptions.