Mariota completed 18-of-26 passes for 253 yards with a TD toss to Josh Huff and ran for 133 yards on 15 carries for the Ducks (11-2), who won 11 games under a first-year coach (Mark Helfrich) for the first time in school history.
Oregon returned a pair of Case McCoy interceptions for touchdowns and limited Texas to 236 total yards on defense.
McCoy went 8-of-17 through the air for just 48 passing yards as the Longhorns (8-5) fell hard in their final game under retiring Coach Mack Brown.
In 16 years guiding Texas, Brown compiled 158 wins, reached a BCS bowl four times and won the national championship in 2005. But his team finished with just eight wins for a fourth straight year.