If both Stanford and Oregon win in their final games next weekend, both will finish with one conference loss, which means Stanford will win the head-to-head matchup and go to the Pac-12 championship for a chance to play in the Rose Bowl.

Stanford (9-2, 7-1) will visit No. 17 UCLA, which defeated No. 21 USC 38-28 earlier in the day to claim the Pac-12 South. Oregon (10-1, 7-1) will play rival Oregon State in the annual Civil War rivalry game in Corvallis.

The loss snapped a 13-game winning streak for the Ducks, which was the longest in the nation coming into Saturday. It was Stanford’s fifth straight win.

Oregon’s loss, coupled with No. 2 Kansas State’s — they were also the top two teams in the BCS standings — means Notre Dame is now the lone unbeaten team in the race for the BCS title game.

The Fighting Irish control their national championship run, with No. 4 Alabama and a couple of other Southeastern Conference teams also in the thick of it.

Oregon was the only Pac-12 team that Stanford hadn’t defeated over the past two seasons. But the Cardinal’s tough defense smothered the highest scoring team in the nation.

Alejandro Maldonado missed a 41-yard field goal for the Ducks to open overtime.

Redshirt freshman Kevin Hogan threw for 211 yards and a game-tying fourth-quarter touchdown for Stanford, while Stepfan Taylor rushed for 161 yards on 33 carries.

Down 14-7, Stanford went for it on fourth-and-1 on the Oregon 12 with 2:17 left in regulation and Ryan Hewitt ran for the first down. Hogan hit Zach Ertz with a 10-yard scoring pass to tie it at 14 with 1:35 to go. Ertz fought to gain control of the ball with a defender as he fell to the turf on top of a Ducks player. The play was initially ruled incomplete, but a video review overturned it for the game-tying touchdown.

Despite a pass interference call gave them a crucial first down, the Ducks were forced to punt on the ensuing series and Stanford took over with 36 seconds to go and the game went to overtime.

The Cardinal had the nation’s best run defense going into the game, allowing an average of just 54.8 yards a game. Oregon meanwhile, had the country’s third-best rushing offense, averaging 325 yards a game.

Stanford held Ducks running back Kenjon Barner, who was averaging 136 yards rushing a game, to just 66 yards. Overall, the Ducks managed only 198 yards on the ground.

Oregon’s top rusher was quarterback Marcus Mariota, who ran for 89 yards. Mariota, a redshirt freshman who had been getting Heisman buzz, threw for 207 yards and a touchdown.

Stanford stopped what appeared to be a sure first-quarter Oregon touchdown drive when Mariota took off on a 77-yard keeper to the Stanford 15. But the Ducks couldn’t get much closer, and Stanford got the stop when Oregon went for it on fourth-and-2 on the Cardinal 7.

Stanford scored first on Hogan’s 1-yard plow into the end zone early in the second quarter.

Oregon tried again on fourth-and-4 midway through the quarter, but was unsuccessful, this time when Mariota’s pass to tight end Colt Lyerla fell incomplete.

When Oregon took over on downs from Stanford on the next series, the Ducks marched 59 yards in three plays — capped by Mariota’s 28-yard touchdown pass to Keanon Lowe — to tie it at 7-all.

Oregon extended its lead to 14-7 on De-Anthony Thomas’ 6-yard scoring run in the third quarter, but missed a chance when Maldonado’s 42-yard field goal attempt went wide right.

Williamson missed a 43-yard field goal attempt for Stanford early in the fourth quarter.