Column: Oregon shows a mean, green streak in Rose Bowl blowout of Florida St.

Florida State rallied from 21 points down to beat Louisville this season, burrowed back to take out Clemson and survived close calls against Miami, Notre Dame and Boston College.

Florida State, it was said, written and reiterated, was the cockroach you could not kill.

Well, the boot heel came down Thursday, in the Rose Bowl, where the Seminoles got squished.

Florida State’s 29-game winning streak was turned over to a green streak of Ducks.

Oregon ended Tallahassee’s two-year tailgater on a crisp, clear day, in bright sunshine, before a crowd of 91,322.

The follow-up investigation on Oregon’s 59-20 win over Florida State will not require CSI Pasadena.

The case was open and shut-you-up.

You simply do not get away with the things Florida State got away with all season. Not against this gaggle of points carnivores.

Florida State, which checks out at 13-1, had been asking for this, and got it.

Oregon (13-1) provided a double-dose of West Coast football pride by advancing to the first College Football Playoff championship game on Jan. 12 in Arlington, Texas.

If the Ducks can promise to play like this a week from Monday, Nike boss Phil Knight can start ordering championship rings . . . or maybe shoestrings?

“Hopefully we can take a little bit of this momentum into the next game,” Oregon quarterback Marcus Mariota said afterward.

Mariota, the Heisman Trophy winner, led an offense that amassed 639 total yards and 7.9 yards per play. He passed for 338 yards and two touchdowns, rushed for 62 and a score and could only be sent to after-school detention for throwing his third interception . . . of the season.

A close, 18-13 game at halftime was ripped apart in the third quarter by four Florida State turnovers — three fumbles and an interception.

What did you expect Oregon would do with those kind of gifts? The Ducks scored four touchdowns, in whirlwind fashion, with Florida State’s defense helpless to stop it.

Defeating Oregon straight up is tough enough. Handing turnovers to the Ducks is like throwing chum to sharks.

The onslaught started harmlessly enough, on Florida State’s first second-half possession, when true freshman running back Dalvin Cook fumbled.

Oregon linebacker Derrick Malone Jr. made a great play, stripping and recovering the ball, and sent the Ducks on their merry way.

Oregon turned the turnover into Royce Freeman’s three-yard scoring run with 11:54 left in the third quarter.

It put Florida State behind by 12 points and into catch-up mode against a team that runs like a roadrunner.

Florida State answered with a promising 75-yard touchdown drive but Mariota answered that with a short toss to Darren Carrington, who put an inside move on safety Tyler Hunter and raced 56 yards for a score.

Florida State might have been able to hang close by exchanging touchdowns but, instead, imploded.

Oregon safety Erick Dargan stripped Cook of his second fumble, with Reggie Daniels recovering.

Old-school coaches like Ohio State’s Woody Hayes used to say you lose one game for every freshman you start.

In the modern game, though, Cook had grown into a late-season weapon who could be trusted under pressure.

Cook just had a really bad third quarter. His second fumble led to another quick Oregon score.

How quick? The Ducks needed two plays and 21 seconds to capitalize, scoring on a 30-yard pass from Mariota to Carrington.

That made it 39-20 with 4:21 left in the quarter. History said you still couldn’t count out Florida State . . . yet. Last year, the Seminoles rallied from 18 down against Auburn to win the national title at the Rose Bowl.

Who knew what quarterback Jameis Winston might pull out of his back pocket?

What no one considered was Winston falling on his pocket in the game-altering moment.

Florida State faced fourth and five at the Oregon 30 when Winston scrambled to buy time in the backfield.

“I was just trying to make a play,” he later said.

Winston, though, slipped off his back foot, like someone had thrown down a banana peel. As the 2013 Heisman winner fell backward the ball flew out of his right hand and bounced to linebacker Tony Washington, who raced 58 yards for the defensive score.

“It was just an unfortunate play, man,” Winston said. “I never thought I would slip, throw the ball backwards.”

It was at that point everyone realized Florida State wasn’t coming back from this deficit.

One of college football’s greatest winning streaks was history. Miami and USC each won 34 straight at the height of their mini-dynasties earlier this century. Miami’s streak crashed against Ohio State in the 2002 title game, while USC’s was stopped three years later at the Rose Bowl, in the title game, against Texas.

Die-hard Florida State fans who thought their team could overcome Oregon’s 45-20 third-quarter lead could only wince over what happened next.

Winston ended the horror-show third by throwing an interception.

The only thing that delayed Oregon’s punctuation point was having to switch sides for the fourth quarter. It was soon thereafter that Mariota raced 23 yards for another score.

It was time to turn out the lights. Mariota was lifted with 9:13 left, giving him almost an extra 10 minutes to rest up for the title game.

Winston, understandably, had a difficult time coming to terms with defeat after winning his first 26 collegiate starts. Winston hadn’t lost a game since 2011, his senior year in high school.

It was Florida State’s first loss in 768 days dating to a late-November 2012 defeat to Florida.

Winston, a competitor to the end, made the 39-point loss sound like a squeaker.

“If everybody in this room just want to be real with themselves, this game could have went either way,” he insisted. “We turned the ball over a lot. We beat ourself.”

More objective voices will remember Oregon wiping the slate clean on the first day of a new year.

Oregon was the better team in a better system. The Ducks, in the old BCS system, never would have been given the chance to prove they were better than Florida State.

The BCS standings would have paired No. 1 Alabama against No. 2 Florida State in the final game.

Oregon would have been third, left to wonder what it might feel like to be 10 days from winning its first national title.

chris.dufresne@latimes.com