Mariota and the second-seeded Ducks (13-1) scored six straight times they touched the ball in the second half, with five of the touchdowns covering at least 21 yards and the last four coming after Florida State turnovers.
In the matchup of Heisman Trophy winners, Jameis Winston matched Mariota's numbers, but the defending national champions were no match for the Ducks. The Pac-12 champions will play the winner of the Sugar Bowl semifinal between Alabama and Ohio State on Jan. 12 in Arlington, Texas.
Third-seeded Florida State's winning streak ends at 29. In Winston's first loss as a college starter, maybe his last game in college, he threw for 348 yards.
No Heisman jinx for Mariota. He was mostly brilliant again. The junior passed for 338 yards and two touchdowns and sprinted in for a 23 yard-touchdown with 13:56 left in the fourth quarter that made it 52-20 and made the Ducks the first team to reach 50 points in Rose Bowl history. This was No. 101.
"59-20, I did not expect that," Oregon defensive end Arik Armstead said.
The Ducks fans spent much of the final quarter mockingly doing the Seminoles' warchant and tomahawk chop. Next stop: The Lone Star state to try to win the program's first national title.
The first playoff game at college football's highest level, the type of postseason game fans have longed for forever, looked like it would be a classic for about two and half quarters.
Under a cloudless sky, on chilly day in Pasadena, the Rose Bowl featured the third matchup of Heisman Trophy winners and a couple of quarterbacks who could be vying to be the first overall pick in April's NFL draft.
Mariota and Winston were both OK in the first half, missing some throws and making some spectacular ones. It was Mariota who threw the only interception, just his third of the season. The late pick didn't hurt the Ducks much because Florida State's Roberto Aguayo missed a 54-yard field goal on the final play of the half.
For the sixth time this season, Florida State was trailing at the half.
And then the hole got deeper.
The Seminoles' first turnover was a huge swing. Freshman Dalvin Cook was stripped by Derrick Malone Jr. with Florida State in Oregon territory. The Ducks quickly flipped the field and Freeman scored his second touchdown of the day from 3 yards out to make it 25-13.
Oregon coach Mark Helfrich had called the Seminoles "unflappable" during the week leading up to the Rose Bowl -- and they showed it on the next drive.
Winston threw an 18-yard touchdown pass to freshman Travis Rudolph. Midway through the third quarter it was 25-20 Oregon and then it was Mariota's turn.
He zipped a pass to Darren Carrington near the sideline and the receiver made one cut and was gone for a 56-yard touchdown that made it 32-20.
Instead of an answer from Florida State, this time another fumble by Cook and the wave of big plays and points that the Ducks do better than any team in the country started rumbling.
Two plays after the turnover, Mariota hit Carrington for a 30-yard touchdown and it was 39-20 and the Rose Bowl, filled mostly with green and yellow, was rumbling, too.