Afterward, Stanford's players cheered wildly in their victorious locker room, even belting out the national anthem at the top of their lungs.
"We celebrate all victories, and this one's a big one," quarterback Kevin Hogan said.
Hogan threw four of his five scoring passes to Montgomery, including a 9-yard completion just before halftime that put Stanford ahead 42-13. The Cardinal (9-2, 7-2 Pac-12) bounced back from last week's loss at USC but needed No. 5 Oregon to lose one of its final two games to win the Pac-12 North. The Ducks lost 42-16 in Tucson, and Stanford's fans led chants of "Arizona! Arizona!"
Stanford beat Oregon, giving the Cardinal the tiebreaker.
Hogan set career highs with 329 yards passing and the five TD passes.
Cal (1-11, 0-9) lost its 10th straight to finish coach Sonny Dykes' disappointing debut year.
"I can make a bunch of excuses, but my job is to get these guys ready to play," Dykes said, "and obviously I haven't."
Michael Rector caught a 45-yard touchdown pass midway through the second quarter for Stanford, while Tyler Gaffney ran for a 58-yard score out of the wildcat formation in the third for a 49-13 lead — giving Stanford its season high for points and most ever in a Big Game. The Cardinal were 31?-point favorites, and the margin of victory was largest in Big Game history.
Other than that, it was Montgomery's day. He tied Darrin Nelson's single-game touchdowns record set at Oregon State in 1981.
He ran for a 31-yard touchdown and caught a 50-yard touchdown pass both in the opening 3 1/2 minutes, then added a 12-yard TD reception with 6:58 to go in the first quarter. On the second play of the second quarter, he made a 72-yard catch and run from Hogan, who was credited with a career-long completion on the play.