BERKELEY, Calif. -- Running back Christian McCaffrey had another record breaking game and the Stanford Cardinal continued their dominance of California on Saturday at Memorial Stadium.

McCaffrey rushed for a school-record 284 yards and three touchdowns, leading Stanford to a 45-31 victory over the Bears on a rainy day in Berkeley.

"What else can you say about Christian McCaffrey that hasn't already been said?" Stanford coach David Shaw said. "Great football player, one of the best in the nation. Offensive line is playing real well, and he's been healthy. And this is what happens when he's healthy. He is special, special, special. He took the game over."

Stanford (8-3, 6-3 Pac-12) defeated Cal for the seventh straight time, matching its school record in the rivalry, and won its fourth straight game this season.

McCaffrey, who carried 31 times, broke his own school rushing record of 243 yards, set last season against USC, and set a Big Game rushing mark in its 119th edition. He also had the longest run of his career, racing 90 yards for a touchdown early in the third quarter.

"It means a lot," McCaffrey said of the Big Game record. "That's a huge honor for me, but that's an honor that I share with the O-line the fullbacks and the receivers and (quarterback) Keller (Chryst) blocking downfield."

Quarterback Davis Webb completed 34 of 57 passes for 393 yards and two touchdowns for Cal (4-7, 2-6), which lost its fourth straight game and was eliminated from contention for a bowl game.

"It (stinks) losing to your rival in Stanford, and the scenario we were in to lose that game, it's not fun for anybody,'' Webb said. "We're a little beat up right now, but this team will be tested for how badly we want to finish the season strong."

Cal wide receiver Chad Hansen had seven catches for 114 yards and two touchdowns, including a 70-yard score in the first quarter. Cal running back Tre Watson rushed for 60 yards and two scores on 11 carries.

Chryst completed 13 of 23 passes for 198 yards and two touchdowns for Stanford, which entered the game at No. 24 in the College Football Playoff rankings. He also ran for a touchdown. Wide receiver JJ Arcega-Whiteside caught four passes for a career-high 107 yards.

McCaffrey scored on Stanford's second play from scrimmage in the second half, extending the lead to 24-14. On second-and-8 from Stanford's 10, he darted through a hole over left guard and raced 90 yards to the end zone.

"Great blocking up front," McCaffrey said. "Had to make the safety miss. And after that there was really no on there. So just turn on the jets and run."

Cal cut Stanford's lead to 24-17 on Matt Anderson's 43-yard field goal with 9:22 left in the third quarter.

McCaffrey scored again with 4:07 left in the third quarter, this time on a 12-yard run up the middle, making it 34-17. But Cal answered with Watson's 8-yard touchdown run with 25 seconds left in the quarter.

Stanford needed only six plays to march 69 yards for McCaffrey's third touchdown of the game, a 1-yard leap, extending its lead to 38-24 with 12:31 left. Chryst's 60-yard pass to Arcega-Whiteside gave Stanford first-and-goal from the 7.

"He's a great player," Cal defensive end DeVante Wilson of McCaffrey. "We just didn't get the job done in stopping him in this game. He's a hell of a player."

Chryst's 30-yard touchdown pass to wide receiver Trenton Irwin increased the Cardinal's lead to 45-24 with 4:17 left to play. The Bears answered with Webb's 16-yard TD strike to Hansen with 3:01 remaining.

McCaffrey rushed for 124 yards on 16 carries in the first half as the Cardinal built a 17-14 lead.

Cal, however, struck first. Hansen caught a quick slant from Webb, knifed through Stanford's secondary and race 70 yards for a touchdown, putting the Bears ahead 7-0 with 11:35 left in the first quarter.

"This team never panics," said Stanford outside linebacker Peter Kalambayi, who had a team-high nine tackles.

Stanford answered with Chryst's 16-yard touchdown run with 11:03 remaining in the quarter.

Cal regained the lead at 14-7 on Watson's 7-yard touchdown run with 13:51 left in the half, capping an 11-play, 83-yard drive. Stanford pulled even when Chryst hit tight end Dalton Schultz with a 9-yard touchdown pass with 8:48 left in the second quarter.

Stanford kicker Conrad Ukropina connected from 40 yards on the first half's final play.

NOTES: Stanford RB Christian McCaffrey moved past Toby Gerhart (3,522) into third place on Stanford's career rushing list with 3,718 career yards. .... WR Chad Hansen became the seventh player in Cal history with at least 1,000 receiving yards in a season. He has 1,093 yards. ... Cal FB/TE Malik McMorris, who weighs 310 pounds, caught his first two passes of the season, including one for 20 yards on a screen during a first-half touchdown drive.