STANFORD — With one minute remaining Saturday in the third quarter of the 116th Big Game, Stanford won the Pac-12 North.

The Cardinal was on its way to a 63-13 victory over Cal — the most points scored by one team in series history — when the stunning result from Tucson became official:

Oregon had lost at Arizona, handing the division title to Stanford.

“It felt great to know we were going to get another opportunity,” said receiver Ty Montgomery, who set a Big Game record with five touchdowns (all in the first half). “But I was focused on this game.”

Cardinal coach David Shaw learned the Ducks had lost from former cornerback Richard Sherman, who was on the sideline because his Seattle Seahawks have a bye this week.

“He tapped me on the shoulder and didn’t say anything, just showed me his phone, which had the score on it,” Shaw said. “Of course, I was a little bit shocked. I thought I was seeing it the wrong way.”

Shaw saw it right: The 10th-ranked Cardinal will play Arizona State, the South champion, on Dec. 7 for the league title and a berth in the Rose Bowl.

The location of the title game has not been determined. If Arizona State beats Arizona next week, the title game will be in Tempe. If ASU loses, the Cardinal (9-2, 7-2 Pac-12) would be the host.

“I’ll have to be thankful for Ka’Deem Carey and RichRod on Thursday,” Stanford linebacker Shayne Skov said of the Arizona tailback and coach Rich Rodriguez. “We were focused on this week and looked up and (Arizona was) winning.”

Stanford’s rowdy locker room celebration — at one point, the players could be heard singing a spirited rendition of the national anthem — was spurred not only by the division title but also its fourth consecutive victory over Cal.

In addition to its record-setting point total, Stanford’s victory margin was the largest in series history.

The Cardinal also established a school record for points in a half (42, in the first) and won its 15th home game in a row.

“Anytime we win the Big Game,” quarterback Kevin Hogan said, “especially with the news we got — we celebrate all victories, and this one’s a huge one.”

The game went as scripted, with Stanford — a 32-point favorite — dominating from the outset.

The only difference was the path the Cardinal took to the end zone.

“We wanted to make them have to execute the passing game, complete passes, and to their credit that’s what they did,” Cal coach Sonny Dykes said.

With Cal loading up the line of scrimmage to stop tailback Tyler Gaffney, the Cardinal used alternate methods to reach the end zone — namely Montgomery.

The junior scored touchdowns the first four times he touched the ball and finished with 191 yards from scrimmage. He tied Darrin Nelson’s school record for most points (30) and touchdowns (five) in a game.

“I knew as an offense we were going to be able to do what we did today,” Montgomery said.

He opened the scoring with a 31-yard touchdown run, then played a private game of catch with Hogan:

Hogan to Montgomery for 50 yards and a touchdown.

Hogan to Montgomery for 12 yards and a touchdown.

Hogan to Montgomery for 72 yards and a touchdown.

Hogan to Montgomery for 9 yards and a touchdown.

“Just getting him the ball, he makes me look good,” said Hogan, who threw for a career-high 329 yards and five touchdowns.

“Really, it was a total team effort today.”

By Stanford — and Arizona.

For more on college sports, see Jon Wilner’s College Hotline at blogs.mercurynews.com/collegesports. Contact him at jwilner@mercurynews.com or 408-920-5716.